[{"related_material":{"record":[{"relation":"earlier_version","id":"186","status":"public"}]},"year":"2022","acknowledgement":"We thank Zdeněk Dvořák, Xavier Goaoc, and Pavel Paták for helpful discussions. We also thank Bojan Mohar, Paul Seymour, Gelasio Salazar, Jim Geelen, and John Maharry for information about their unpublished results related to Conjecture 3.1. Finally we thank the reviewers for corrections and suggestions for improving the presentation.\r\nSupported by Austrian Science Fund (FWF): M2281-N35. Supported by project 19-04113Y of the Czech Science Foundation (GAČR), by the Czech-French collaboration project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM), and by Charles University project UNCE/SCI/004.","citation":{"mla":"Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” Discrete and Computational Geometry, vol. 68, Springer Nature, 2022, pp. 425–47, doi:10.1007/s00454-022-00412-w.","chicago":"Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00412-w.","ista":"Fulek R, Kynčl J. 2022. The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. 68, 425–447.","short":"R. Fulek, J. Kynčl, Discrete and Computational Geometry 68 (2022) 425–447.","ieee":"R. Fulek and J. Kynčl, “The Z2-Genus of Kuratowski minors,” Discrete and Computational Geometry, vol. 68. Springer Nature, pp. 425–447, 2022.","ama":"Fulek R, Kynčl J. The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. 2022;68:425-447. doi:10.1007/s00454-022-00412-w","apa":"Fulek, R., & Kynčl, J. (2022). The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00412-w"},"date_created":"2022-07-17T22:01:56Z","doi":"10.1007/s00454-022-00412-w","article_type":"original","_id":"11593","abstract":[{"text":"A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The Z2 -genus of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t×t grid or one of the following so-called t -Kuratowski graphs: K3,t, or t copies of K5 or K3,3 sharing at most two common vertices. We show that the Z2-genus of graphs in these families is unbounded in t; in fact, equal to their genus. Together, this implies that the genus of a graph is bounded from above by a function of its Z2-genus, solving a problem posed by Schaefer and Štefankovič, and giving an approximate version of the Hanani–Tutte theorem on orientable surfaces. We also obtain an analogous result for Euler genus and Euler Z2-genus of graphs.","lang":"eng"}],"external_id":{"arxiv":["1803.05085"],"isi":["000825014500001"]},"publication_status":"published","date_published":"2022-09-01T00:00:00Z","publisher":"Springer Nature","volume":68,"quality_controlled":"1","department":[{"_id":"UlWa"}],"page":"425-447","project":[{"grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs"}],"isi":1,"intvolume":" 68","scopus_import":"1","article_processing_charge":"No","date_updated":"2023-08-14T12:43:52Z","oa":1,"title":"The Z2-Genus of Kuratowski minors","publication":"Discrete and Computational Geometry","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.05085"}],"day":"01","oa_version":"Preprint","arxiv":1,"author":[{"full_name":"Fulek, Radoslav","first_name":"Radoslav","orcid":"0000-0001-8485-1774","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Kynčl","first_name":"Jan","full_name":"Kynčl, Jan"}],"status":"public","type":"journal_article"},{"doi":"10.15479/at:ista:11777","file_date_updated":"2022-08-11T16:09:19Z","_id":"11777","ec_funded":1,"degree_awarded":"PhD","date_created":"2022-08-10T15:51:19Z","citation":{"apa":"Wild, P. (2022). High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology. https://doi.org/10.15479/at:ista:11777","chicago":"Wild, Pascal. “High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes.” Institute of Science and Technology, 2022. https://doi.org/10.15479/at:ista:11777.","mla":"Wild, Pascal. High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes. Institute of Science and Technology, 2022, doi:10.15479/at:ista:11777.","ista":"Wild P. 2022. High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology.","ama":"Wild P. High-dimensional expansion and crossing numbers of simplicial complexes. 2022. doi:10.15479/at:ista:11777","ieee":"P. Wild, “High-dimensional expansion and crossing numbers of simplicial complexes,” Institute of Science and Technology, 2022.","short":"P. Wild, High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes, Institute of Science and Technology, 2022."},"year":"2022","department":[{"_id":"GradSch"},{"_id":"UlWa"}],"page":"170","publisher":"Institute of Science and Technology","supervisor":[{"last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","full_name":"Wagner, Uli"}],"date_published":"2022-08-11T00:00:00Z","project":[{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"abstract":[{"lang":"eng","text":"In this dissertation we study coboundary expansion of simplicial complex with a view of giving geometric applications.\r\nOur main novel tool is an equivariant version of Gromov's celebrated Topological Overlap Theorem. The equivariant topological overlap theorem leads to various geometric applications including a quantitative non-embeddability result for sufficiently thick buildings (which partially resolves a conjecture of Tancer and Vorwerk) and an improved lower bound on the pair-crossing number of (bounded degree) expander graphs. Additionally, we will give new proofs for several known lower bounds for geometric problems such as the number of Tverberg partitions or the crossing number of complete bipartite graphs.\r\nFor the aforementioned applications one is naturally lead to study expansion properties of joins of simplicial complexes. In the presence of a special certificate for expansion (as it is the case, e.g., for spherical buildings), the join of two expanders is an expander. On the flip-side, we report quite some evidence that coboundary expansion exhibits very non-product-like behaviour under taking joins. For instance, we exhibit infinite families of graphs $(G_n)_{n\\in \\mathbb{N}}$ and $(H_n)_{n\\in\\mathbb{N}}$ whose join $G_n*H_n$ has expansion of lower order than the product of the expansion constant of the graphs. Moreover, we show an upper bound of $(d+1)/2^d$ on the normalized coboundary expansion constants for the complete multipartite complex $[n]^{*(d+1)}$ (under a mild divisibility condition on $n$).\r\nVia the probabilistic method the latter result extends to an upper bound of $(d+1)/2^d+\\varepsilon$ on the coboundary expansion constant of the spherical building associated with $\\mathrm{PGL}_{d+2}(\\mathbb{F}_q)$ for any $\\varepsilon>0$ and sufficiently large $q=q(\\varepsilon)$. This disproves a conjecture of Lubotzky, Meshulam and Mozes -- in a rather strong sense.\r\nBy improving on existing lower bounds we make further progress towards closing the gap between the known lower and upper bounds on the coboundary expansion constants of $[n]^{*(d+1)}$. The best improvements we achieve using computer-aided proofs and flag algebras. The exact value even for the complete $3$-partite $2$-dimensional complex $[n]^{*3}$ remains unknown but we are happy to conjecture a precise value for every $n$. %Moreover, we show that a previously shown lower bound on the expansion constant of the spherical building associated with $\\mathrm{PGL}_{2}(\\mathbb{F}_q)$ is not tight.\r\nIn a loosely structured, last chapter of this thesis we collect further smaller observations related to expansion. We point out a link between discrete Morse theory and a technique for showing coboundary expansion, elaborate a bit on the hardness of computing coboundary expansion constants, propose a new criterion for coboundary expansion (in a very dense setting) and give one way of making the folklore result that expansion of links is a necessary condition for a simplicial complex to be an expander precise."}],"ddc":["500","516","514"],"publication_status":"published","language":[{"iso":"eng"}],"has_accepted_license":"1","title":"High-dimensional expansion and crossing numbers of simplicial complexes","oa":1,"date_updated":"2023-06-22T09:56:36Z","article_processing_charge":"No","alternative_title":["ISTA Thesis"],"status":"public","type":"dissertation","day":"11","oa_version":"Published Version","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","file":[{"date_updated":"2022-08-10T15:34:04Z","date_created":"2022-08-10T15:34:04Z","file_name":"flags.py","file_id":"11780","checksum":"f5f3af1fb7c8a24b71ddc88ad7f7c5b4","description":"Code for computer-assisted proofs in Section 8.4.7 in Thesis","content_type":"text/x-python","access_level":"open_access","relation":"supplementary_material","file_size":16828,"creator":"pwild"},{"date_updated":"2022-08-10T15:34:10Z","date_created":"2022-08-10T15:34:10Z","file_name":"lowerbound.cpp","file_id":"11781","checksum":"1f7c12dfe3bdaa9b147e4fbc3d34e3d5","description":"Code for proof of Lemma 8.20 in Thesis","relation":"supplementary_material","content_type":"text/x-c++src","access_level":"open_access","file_size":12226,"creator":"pwild"},{"description":"Code for proof of Proposition 7.9 in Thesis","file_name":"upperbound.py","file_id":"11782","checksum":"4cf81455c49e5dec3b9b2e3980137eeb","date_created":"2022-08-10T15:34:17Z","date_updated":"2022-08-10T15:34:17Z","creator":"pwild","file_size":3240,"relation":"supplementary_material","access_level":"open_access","content_type":"text/x-python"},{"date_created":"2022-08-11T16:08:33Z","title":"High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes","date_updated":"2022-08-11T16:08:33Z","file_name":"finalthesisPascalWildPDFA.pdf","checksum":"4e96575b10cbe4e0d0db2045b2847774","file_id":"11809","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":5086282,"creator":"pwild"},{"creator":"pwild","relation":"source_file","content_type":"application/zip","access_level":"closed","file_size":18150068,"file_name":"ThesisSubmission.zip","checksum":"92d94842a1fb6dca5808448137573b2e","file_id":"11810","date_created":"2022-08-11T16:09:19Z","date_updated":"2022-08-11T16:09:19Z"}],"month":"08","publication_identifier":{"isbn":["978-3-99078-021-3"],"issn":["2663-337X"]},"author":[{"id":"4C20D868-F248-11E8-B48F-1D18A9856A87","last_name":"Wild","full_name":"Wild, Pascal","first_name":"Pascal"}]},{"intvolume":" 26","has_accepted_license":"1","scopus_import":"1","title":"On compatible matchings","oa":1,"date_updated":"2023-02-23T13:54:21Z","issue":"2","article_processing_charge":"No","publication":"Journal of Graph Algorithms and Applications","language":[{"iso":"eng"}],"day":"01","oa_version":"Published Version","file":[{"file_id":"11940","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","checksum":"dc6e255e3558faff924fd9e370886c11","success":1,"date_updated":"2022-08-22T06:42:42Z","date_created":"2022-08-22T06:42:42Z","creator":"dernst","file_size":694538,"relation":"main_file","content_type":"application/pdf","access_level":"open_access"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1526-1719"]},"month":"06","author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M"},{"last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","full_name":"Masárová, Zuzana"},{"full_name":"Parada, Irene","first_name":"Irene","last_name":"Parada"},{"full_name":"Perz, Daniel","first_name":"Daniel","last_name":"Perz"},{"last_name":"Pilz","first_name":"Alexander","full_name":"Pilz, Alexander"},{"id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","first_name":"Josef"},{"last_name":"Vogtenhuber","first_name":"Birgit","full_name":"Vogtenhuber, Birgit"}],"arxiv":1,"type":"journal_article","status":"public","ec_funded":1,"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9296"}]},"date_created":"2022-08-21T22:01:56Z","citation":{"ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591","ieee":"O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591"},"acknowledgement":"A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","year":"2022","doi":"10.7155/jgaa.00591","file_date_updated":"2022-08-22T06:42:42Z","article_type":"original","_id":"11938","external_id":{"arxiv":["2101.03928"]},"abstract":[{"text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge.","lang":"eng"}],"ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"page":"225-240","quality_controlled":"1","volume":26,"publisher":"Brown University","date_published":"2022-06-01T00:00:00Z","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23"},{"call_identifier":"FWF","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407"}]},{"publication":"ACM SIGLOG News","language":[{"iso":"eng"}],"intvolume":" 9","issue":"3","article_processing_charge":"No","date_updated":"2022-09-05T08:19:38Z","oa":1,"title":"An invitation to the promise constraint satisfaction problem","type":"journal_article","status":"public","publication_identifier":{"issn":["2372-3491"]},"month":"07","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/2208.13538"}],"day":"01","oa_version":"Preprint","arxiv":1,"author":[{"last_name":"Krokhin","full_name":"Krokhin, Andrei","first_name":"Andrei"},{"last_name":"Opršal","id":"ec596741-c539-11ec-b829-c79322a91242","orcid":"0000-0003-1245-3456","first_name":"Jakub","full_name":"Opršal, Jakub"}],"doi":"10.1145/3559736.3559740","article_type":"original","_id":"11991","year":"2022","date_created":"2022-08-27T11:23:37Z","citation":{"apa":"Krokhin, A., & Opršal, J. (2022). An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. Association for Computing Machinery. https://doi.org/10.1145/3559736.3559740","ista":"Krokhin A, Opršal J. 2022. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 9(3), 30–59.","chicago":"Krokhin, Andrei, and Jakub Opršal. “An Invitation to the Promise Constraint Satisfaction Problem.” ACM SIGLOG News. Association for Computing Machinery, 2022. https://doi.org/10.1145/3559736.3559740.","mla":"Krokhin, Andrei, and Jakub Opršal. “An Invitation to the Promise Constraint Satisfaction Problem.” ACM SIGLOG News, vol. 9, no. 3, Association for Computing Machinery, 2022, pp. 30–59, doi:10.1145/3559736.3559740.","short":"A. Krokhin, J. Opršal, ACM SIGLOG News 9 (2022) 30–59.","ieee":"A. Krokhin and J. Opršal, “An invitation to the promise constraint satisfaction problem,” ACM SIGLOG News, vol. 9, no. 3. Association for Computing Machinery, pp. 30–59, 2022.","ama":"Krokhin A, Opršal J. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 2022;9(3):30-59. doi:10.1145/3559736.3559740"},"date_published":"2022-07-01T00:00:00Z","publisher":"Association for Computing Machinery","quality_controlled":"1","volume":9,"page":"30-59","department":[{"_id":"UlWa"}],"abstract":[{"text":"The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the Dichotomy Conjecture has been proved in 2017 independently by Bulatov and Zhuk. At about the same time, a vast generalisation of CSP, called promise CSP, has started to gain prominence. In this survey, we explain the importance of promise CSP and highlight many new very interesting features that the study of promise CSP has brought to light. The complexity classification quest for the promise CSP is wide open, and we argue that, despite the promise CSP being more general, this quest is rather more accessible to a wide range of researchers than the dichotomy-led study of the CSP has been.","lang":"eng"}],"external_id":{"arxiv":["2208.13538"]},"publication_status":"published"},{"related_material":{"record":[{"status":"public","id":"7807","relation":"earlier_version"},{"status":"public","id":"7990","relation":"earlier_version"}]},"year":"2022","acknowledgement":"This is a full and revised version of [38] (on partial triangulations) in Proceedings of the 36th Annual International Symposium on Computational Geometry (SoCG‘20) and of some of the results in [37] (on full triangulations) in Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA‘20).\r\nThis research started at the 11th Gremo’s Workshop on Open Problems (GWOP), Alp Sellamatt, Switzerland, June 24–28, 2013, motivated by a question posed by Filip Mori´c on full triangulations. Research was supported by the Swiss National Science Foundation within the collaborative DACH project Arrangements and Drawings as SNSF Project 200021E-171681, and by IST Austria and Berlin Free University during a sabbatical stay of the second author. We thank Michael Joswig, Jesús De Loera, and Francisco Santos for helpful discussions on the topics of this paper, and Daniel Bertschinger and Valentin Stoppiello for carefully reading earlier versions and for many helpful comments.\r\nOpen access funding provided by the Swiss Federal Institute of Technology Zürich","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"citation":{"mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” Discrete & Computational Geometry, vol. 68, no. 4, Springer Nature, 2022, pp. 1227–84, doi:10.1007/s00454-022-00436-2.","chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” Discrete & Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00436-2.","ista":"Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 68(4), 1227–1284.","short":"U. Wagner, E. Welzl, Discrete & Computational Geometry 68 (2022) 1227–1284.","ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane,” Discrete & Computational Geometry, vol. 68, no. 4. Springer Nature, pp. 1227–1284, 2022.","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 2022;68(4):1227-1284. doi:10.1007/s00454-022-00436-2","apa":"Wagner, U., & Welzl, E. (2022). Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00436-2"},"date_created":"2023-01-12T12:02:28Z","doi":"10.1007/s00454-022-00436-2","article_type":"original","_id":"12129","file_date_updated":"2023-01-23T11:10:03Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"abstract":[{"text":"Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.","lang":"eng"}],"external_id":{"isi":["000883222200003"]},"publication_status":"published","date_published":"2022-11-14T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":68,"page":"1227-1284","department":[{"_id":"UlWa"}],"isi":1,"has_accepted_license":"1","intvolume":" 68","scopus_import":"1","article_processing_charge":"No","issue":"4","oa":1,"date_updated":"2023-08-04T08:51:08Z","title":"Connectivity of triangulation flip graphs in the plane","publication":"Discrete & Computational Geometry","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"11","file":[{"success":1,"checksum":"307e879d09e52eddf5b225d0aaa9213a","file_name":"2022_DiscreteCompGeometry_Wagner.pdf","file_id":"12345","date_created":"2023-01-23T11:10:03Z","date_updated":"2023-01-23T11:10:03Z","creator":"dernst","access_level":"open_access","file_size":1747581,"content_type":"application/pdf","relation":"main_file"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","day":"14","author":[{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"type":"journal_article","status":"public"},{"citation":{"apa":"Ivanov, G. (2021). No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12449","short":"G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641.","ieee":"G. Ivanov, “No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p,” Bulletin of the London Mathematical Society, vol. 53, no. 2. London Mathematical Society, pp. 631–641, 2021.","ama":"Ivanov G. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. 2021;53(2):631-641. doi:10.1112/blms.12449","mla":"Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” Bulletin of the London Mathematical Society, vol. 53, no. 2, London Mathematical Society, 2021, pp. 631–41, doi:10.1112/blms.12449.","chicago":"Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” Bulletin of the London Mathematical Society. London Mathematical Society, 2021. https://doi.org/10.1112/blms.12449.","ista":"Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. 53(2), 631–641."},"date_created":"2021-01-24T23:01:08Z","year":"2021","acknowledgement":"I wish to thank Imre Bárány for bringing the problem to my attention. I am grateful to Marton Naszódi and Igor Tsiutsiurupa for useful remarks and help with the text.\r\nThe author acknowledges the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no 075‐15‐2019‐1926.","article_type":"original","_id":"9037","file_date_updated":"2021-08-06T09:59:45Z","doi":"10.1112/blms.12449","publication_status":"published","abstract":[{"text":"We continue our study of ‘no‐dimension’ analogues of basic theorems in combinatorial and convex geometry in Banach spaces. We generalize some results of the paper (Adiprasito, Bárány and Mustafa, ‘Theorems of Carathéodory, Helly, and Tverberg without dimension’, Proceedings of the Thirtieth Annual ACM‐SIAM Symposium on Discrete Algorithms (Society for Industrial and Applied Mathematics, San Diego, California, 2019) 2350–2360) and prove no‐dimension versions of the colored Tverberg theorem, the selection lemma and the weak 𝜀 ‐net theorem in Banach spaces of type 𝑝>1 . To prove these results, we use the original ideas of Adiprasito, Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon theorem and slightly modified version of the celebrated Maurey lemma.","lang":"eng"}],"external_id":{"arxiv":["1912.08561"],"isi":["000607265100001"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"ddc":["510"],"volume":53,"quality_controlled":"1","department":[{"_id":"UlWa"}],"page":"631-641","date_published":"2021-04-01T00:00:00Z","publisher":"London Mathematical Society","title":"No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p","issue":"2","article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2023-08-07T13:35:20Z","has_accepted_license":"1","scopus_import":"1","intvolume":" 53","isi":1,"language":[{"iso":"eng"}],"publication":"Bulletin of the London Mathematical Society","arxiv":1,"author":[{"first_name":"Grigory","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov"}],"file":[{"relation":"main_file","access_level":"open_access","file_size":194550,"content_type":"application/pdf","creator":"kschuh","date_updated":"2021-08-06T09:59:45Z","date_created":"2021-08-06T09:59:45Z","file_name":"2021_BLMS_Ivanov.pdf","checksum":"e6ceaa6470d835eb4c211cbdd38fdfd1","file_id":"9796","success":1}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","oa_version":"Published Version","month":"04","publication_identifier":{"issn":["00246093"],"eissn":["14692120"]},"status":"public","type":"journal_article"},{"language":[{"iso":"eng"}],"publication":"Discrete Mathematics","date_updated":"2023-08-07T13:40:37Z","oa":1,"article_processing_charge":"No","issue":"5","title":"On the volume of projections of the cross-polytope","isi":1,"intvolume":" 344","scopus_import":"1","type":"journal_article","status":"public","author":[{"full_name":"Ivanov, Grigory","first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov"}],"arxiv":1,"month":"05","publication_identifier":{"issn":["0012365X"]},"oa_version":"Preprint","day":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.09165"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","_id":"9098","doi":"10.1016/j.disc.2021.112312","acknowledgement":"Research was supported by the Russian Foundation for Basic Research, project 18-01-00036A (Theorems 1.5 and 5.3) and by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926 (Theorems 1.2 and 7.3).","year":"2021","date_created":"2021-02-07T23:01:12Z","citation":{"ama":"Ivanov G. On the volume of projections of the cross-polytope. Discrete Mathematics. 2021;344(5). doi:10.1016/j.disc.2021.112312","ieee":"G. Ivanov, “On the volume of projections of the cross-polytope,” Discrete Mathematics, vol. 344, no. 5. Elsevier, 2021.","short":"G. Ivanov, Discrete Mathematics 344 (2021).","mla":"Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” Discrete Mathematics, vol. 344, no. 5, 112312, Elsevier, 2021, doi:10.1016/j.disc.2021.112312.","ista":"Ivanov G. 2021. On the volume of projections of the cross-polytope. Discrete Mathematics. 344(5), 112312.","chicago":"Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” Discrete Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.disc.2021.112312.","apa":"Ivanov, G. (2021). On the volume of projections of the cross-polytope. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2021.112312"},"article_number":"112312","publisher":"Elsevier","date_published":"2021-05-01T00:00:00Z","department":[{"_id":"UlWa"}],"volume":344,"quality_controlled":"1","publication_status":"published","external_id":{"arxiv":["1808.09165"],"isi":["000633365200001"]},"abstract":[{"text":"We study properties of the volume of projections of the n-dimensional\r\ncross-polytope $\\crosp^n = \\{ x \\in \\R^n \\mid |x_1| + \\dots + |x_n| \\leqslant 1\\}.$ We prove that the projection of $\\crosp^n$ onto a k-dimensional coordinate subspace has the maximum possible volume for k=2 and for k=3.\r\nWe obtain the exact lower bound on the volume of such a projection onto a two-dimensional plane. Also, we show that there exist local maxima which are not global ones for the volume of a projection of $\\crosp^n$ onto a k-dimensional subspace for any n>k⩾2.","lang":"eng"}]},{"_id":"9295","article_type":"original","doi":"10.1002/jgt.22665","date_created":"2021-03-28T22:01:41Z","citation":{"ista":"Arroyo Guevara AM, Mcquillan D, Richter RB, Salazar G, Sullivan M. 2021. Drawings of complete graphs in the projective plane. Journal of Graph Theory. 97(3), 426–440.","mla":"Arroyo Guevara, Alan M., et al. “Drawings of Complete Graphs in the Projective Plane.” Journal of Graph Theory, vol. 97, no. 3, Wiley, 2021, pp. 426–40, doi:10.1002/jgt.22665.","chicago":"Arroyo Guevara, Alan M, Dan Mcquillan, R. Bruce Richter, Gelasio Salazar, and Matthew Sullivan. “Drawings of Complete Graphs in the Projective Plane.” Journal of Graph Theory. Wiley, 2021. https://doi.org/10.1002/jgt.22665.","short":"A.M. Arroyo Guevara, D. Mcquillan, R.B. Richter, G. Salazar, M. Sullivan, Journal of Graph Theory 97 (2021) 426–440.","ama":"Arroyo Guevara AM, Mcquillan D, Richter RB, Salazar G, Sullivan M. Drawings of complete graphs in the projective plane. Journal of Graph Theory. 2021;97(3):426-440. doi:10.1002/jgt.22665","ieee":"A. M. Arroyo Guevara, D. Mcquillan, R. B. Richter, G. Salazar, and M. Sullivan, “Drawings of complete graphs in the projective plane,” Journal of Graph Theory, vol. 97, no. 3. Wiley, pp. 426–440, 2021.","apa":"Arroyo Guevara, A. M., Mcquillan, D., Richter, R. B., Salazar, G., & Sullivan, M. (2021). Drawings of complete graphs in the projective plane. Journal of Graph Theory. Wiley. https://doi.org/10.1002/jgt.22665"},"acknowledgement":"We thank two reviewers for their corrections and suggestions on the original version of this\r\npaper. This project has received funding from NSERC Grant 50503-10940-500 and from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No 754411, IST, Klosterneuburg, Austria.","year":"2021","ec_funded":1,"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"UlWa"}],"page":"426-440","volume":97,"quality_controlled":"1","publisher":"Wiley","date_published":"2021-03-23T00:00:00Z","publication_status":"published","external_id":{"isi":["000631693200001"],"arxiv":["2002.02287"]},"abstract":[{"lang":"eng","text":"Hill's Conjecture states that the crossing number cr(𝐾𝑛) of the complete graph 𝐾𝑛 in the plane (equivalently, the sphere) is 14⌊𝑛2⌋⌊𝑛−12⌋⌊𝑛−22⌋⌊𝑛−32⌋=𝑛4/64+𝑂(𝑛3) . Moon proved that the expected number of crossings in a spherical drawing in which the points are randomly distributed and joined by geodesics is precisely 𝑛4/64+𝑂(𝑛3) , thus matching asymptotically the conjectured value of cr(𝐾𝑛) . Let cr𝑃(𝐺) denote the crossing number of a graph 𝐺 in the projective plane. Recently, Elkies proved that the expected number of crossings in a naturally defined random projective plane drawing of 𝐾𝑛 is (𝑛4/8𝜋2)+𝑂(𝑛3) . In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked if lim𝑛→∞ cr𝑃(𝐾𝑛)/𝑛4=1/8𝜋2 . We construct drawings of 𝐾𝑛 in the projective plane that disprove this."}],"language":[{"iso":"eng"}],"publication":"Journal of Graph Theory","title":"Drawings of complete graphs in the projective plane","date_updated":"2023-08-07T14:26:15Z","oa":1,"issue":"3","article_processing_charge":"No","scopus_import":"1","intvolume":" 97","isi":1,"type":"journal_article","status":"public","author":[{"first_name":"Alan M","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","orcid":"0000-0003-2401-8670"},{"full_name":"Mcquillan, Dan","first_name":"Dan","last_name":"Mcquillan"},{"last_name":"Richter","full_name":"Richter, R. Bruce","first_name":"R. Bruce"},{"full_name":"Salazar, Gelasio","first_name":"Gelasio","last_name":"Salazar"},{"last_name":"Sullivan","first_name":"Matthew","full_name":"Sullivan, Matthew"}],"arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.02287"}],"day":"23","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["1097-0118"],"issn":["0364-9024"]},"month":"03"},{"doi":"10.1007/978-3-030-68211-8_18","_id":"9296","related_material":{"record":[{"status":"public","relation":"later_version","id":"11938"}]},"ec_funded":1,"year":"2021","acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","citation":{"ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","ieee":"O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18"},"date_created":"2021-03-28T22:01:41Z","date_published":"2021-02-16T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":12635,"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"page":"221-233","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","call_identifier":"FWF","name":"Game Theory"}],"abstract":[{"lang":"eng","text":" matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge."}],"external_id":{"arxiv":["2101.03928"]},"publication_status":"published","publication":"15th International Conference on Algorithms and Computation","language":[{"iso":"eng"}],"scopus_import":"1","intvolume":" 12635","article_processing_charge":"No","oa":1,"date_updated":"2023-02-21T16:33:44Z","title":"On compatible matchings","status":"public","type":"conference","alternative_title":["LNCS"],"publication_identifier":{"isbn":["9783030682101"],"eissn":["16113349"],"issn":["03029743"]},"month":"02","conference":{"location":"Yangon, Myanmar","end_date":"2021-03-02","name":"WALCOM: Algorithms and Computation","start_date":"2021-02-28"},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2101.03928","open_access":"1"}],"day":"16","arxiv":1,"author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M","full_name":"Arroyo Guevara, Alan M"},{"first_name":"Zuzana","full_name":"Masárová, Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322"},{"full_name":"Parada, Irene","first_name":"Irene","last_name":"Parada"},{"full_name":"Perz, Daniel","first_name":"Daniel","last_name":"Perz"},{"last_name":"Pilz","full_name":"Pilz, Alexander","first_name":"Alexander"},{"orcid":"0000-0002-1097-9684","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef","first_name":"Josef"},{"first_name":"Birgit","full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber"}]},{"language":[{"iso":"eng"}],"publication":"Set-Valued and Variational Analysis","title":"Rectifiable curves in proximally smooth sets","article_processing_charge":"No","oa":1,"date_updated":"2023-08-14T08:11:38Z","scopus_import":"1","isi":1,"type":"journal_article","status":"public","arxiv":1,"author":[{"last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory","full_name":"Ivanov, Grigory"},{"last_name":"Lopushanski","first_name":"Mariana S.","full_name":"Lopushanski, Mariana S."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/2012.10691","open_access":"1"}],"oa_version":"Published Version","day":"09","publication_identifier":{"eissn":["1877-0541"],"issn":["0927-6947"]},"month":"10","_id":"10181","article_type":"original","doi":"10.1007/s11228-021-00612-1","date_created":"2021-10-24T22:01:35Z","citation":{"apa":"Ivanov, G., & Lopushanski, M. S. (2021). Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis. Springer Nature. https://doi.org/10.1007/s11228-021-00612-1","mla":"Ivanov, Grigory, and Mariana S. Lopushanski. “Rectifiable Curves in Proximally Smooth Sets.” Set-Valued and Variational Analysis, Springer Nature, 2021, doi:10.1007/s11228-021-00612-1.","ista":"Ivanov G, Lopushanski MS. 2021. Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis.","chicago":"Ivanov, Grigory, and Mariana S. Lopushanski. “Rectifiable Curves in Proximally Smooth Sets.” Set-Valued and Variational Analysis. Springer Nature, 2021. https://doi.org/10.1007/s11228-021-00612-1.","short":"G. Ivanov, M.S. Lopushanski, Set-Valued and Variational Analysis (2021).","ieee":"G. Ivanov and M. S. Lopushanski, “Rectifiable curves in proximally smooth sets,” Set-Valued and Variational Analysis. Springer Nature, 2021.","ama":"Ivanov G, Lopushanski MS. Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis. 2021. doi:10.1007/s11228-021-00612-1"},"year":"2021","acknowledgement":"Theorem 2 was obtained at Steklov Mathematical Institute RAS and supported by Russian Science Foundation, grant N 19-11-00087.","quality_controlled":"1","department":[{"_id":"UlWa"}],"date_published":"2021-10-09T00:00:00Z","publisher":"Springer Nature","publication_status":"published","abstract":[{"text":"In this article we study some geometric properties of proximally smooth sets. First, we introduce a modification of the metric projection and prove its existence. Then we provide an algorithm for constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space, with the moduli of smoothness and convexity of power type. Our algorithm returns a reasonably short curve between two sufficiently close points of a proximally smooth set, is iterative and uses our modification of the metric projection. We estimate the length of the constructed curve and its deviation from the segment with the same endpoints. These estimates coincide up to a constant factor with those for the geodesics in a proximally smooth set in a Hilbert space.","lang":"eng"}],"external_id":{"arxiv":["2012.10691"],"isi":["000705774800001"]}},{"doi":"10.1007/s11856-021-2216-z","_id":"10220","article_type":"original","related_material":{"record":[{"status":"public","id":"8183","relation":"earlier_version"},{"status":"public","id":"9308","relation":"earlier_version"}]},"year":"2021","acknowledgement":"Research supported by the Swiss National Science Foundation (Project SNSF-PP00P2-138948), by the Austrian Science Fund (FWF Project P31312-N35), by the Russian Foundation for Basic Research (Grants No. 15-01-06302 and 19-01-00169), by a Simons-IUM Fellowship, and by the D. Zimin Dynasty Foundation Grant. We would like to thank E. Alkin, A. Klyachko, V. Krushkal, S. Melikhov, M. Tancer, P. Teichner and anonymous referees for helpful comments and discussions.","citation":{"short":"S. Avvakumov, I. Mabillard, A.B. Skopenkov, U. Wagner, Israel Journal of Mathematics 245 (2021) 501–534.","ieee":"S. Avvakumov, I. Mabillard, A. B. Skopenkov, and U. Wagner, “Eliminating higher-multiplicity intersections. III. Codimension 2,” Israel Journal of Mathematics, vol. 245. Springer Nature, pp. 501–534, 2021.","ama":"Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 2021;245:501–534. doi:10.1007/s11856-021-2216-z","mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel Journal of Mathematics, vol. 245, Springer Nature, 2021, pp. 501–534, doi:10.1007/s11856-021-2216-z.","ista":"Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. 2021. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 245, 501–534.","chicago":"Avvakumov, Sergey, Isaac Mabillard, Arkadiy B. Skopenkov, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s11856-021-2216-z.","apa":"Avvakumov, S., Mabillard, I., Skopenkov, A. B., & Wagner, U. (2021). Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-021-2216-z"},"date_created":"2021-11-07T23:01:24Z","date_published":"2021-10-30T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":245,"department":[{"_id":"UlWa"}],"page":"501–534 ","project":[{"grant_number":"P31312","_id":"26611F5C-B435-11E9-9278-68D0E5697425","name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF"}],"abstract":[{"text":"We study conditions under which a finite simplicial complex K can be mapped to ℝd without higher-multiplicity intersections. An almost r-embedding is a map f: K → ℝd such that the images of any r pairwise disjoint simplices of K do not have a common point. We show that if r is not a prime power and d ≥ 2r + 1, then there is a counterexample to the topological Tverberg conjecture, i.e., there is an almost r-embedding of the (d +1)(r − 1)-simplex in ℝd. This improves on previous constructions of counterexamples (for d ≥ 3r) based on a series of papers by M. Özaydin, M. Gromov, P. Blagojević, F. Frick, G. Ziegler, and the second and fourth present authors.\r\n\r\nThe counterexamples are obtained by proving the following algebraic criterion in codimension 2: If r ≥ 3 and if K is a finite 2(r − 1)-complex, then there exists an almost r-embedding K → ℝ2r if and only if there exists a general position PL map f: K → ℝ2r such that the algebraic intersection number of the f-images of any r pairwise disjoint simplices of K is zero. This result can be restated in terms of a cohomological obstruction and extends an analogous codimension 3 criterion by the second and fourth authors. As another application, we classify ornaments f: S3 ⊔ S3 ⊔ S3 → ℝ5 up to ornament concordance.\r\n\r\nIt follows from work of M. Freedman, V. Krushkal and P. Teichner that the analogous criterion for r = 2 is false. We prove a lemma on singular higher-dimensional Borromean rings, yielding an elementary proof of the counterexample.","lang":"eng"}],"external_id":{"arxiv":["1511.03501"],"isi":["000712942100013"]},"publication_status":"published","publication":"Israel Journal of Mathematics","language":[{"iso":"eng"}],"isi":1,"scopus_import":"1","intvolume":" 245","article_processing_charge":"No","date_updated":"2023-08-14T11:43:55Z","oa":1,"title":"Eliminating higher-multiplicity intersections. III. Codimension 2","status":"public","type":"journal_article","month":"10","publication_identifier":{"eissn":["1565-8511"],"issn":["0021-2172"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","day":"30","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.03501"}],"arxiv":1,"author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","full_name":"Avvakumov, Sergey","first_name":"Sergey"},{"last_name":"Mabillard","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","full_name":"Mabillard, Isaac","first_name":"Isaac"},{"first_name":"Arkadiy B.","full_name":"Skopenkov, Arkadiy B.","last_name":"Skopenkov"},{"first_name":"Uli","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}]},{"scopus_import":"1","intvolume":" 35","isi":1,"title":"Extending drawings of complete graphs into arrangements of pseudocircles","oa":1,"date_updated":"2023-08-08T13:58:12Z","article_processing_charge":"No","issue":"2","publication":"SIAM Journal on Discrete Mathematics","language":[{"iso":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2001.06053","open_access":"1"}],"day":"20","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"05","publication_identifier":{"issn":["08954801"]},"author":[{"last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M"},{"last_name":"Richter","full_name":"Richter, R. Bruce","first_name":"R. Bruce"},{"last_name":"Sunohara","full_name":"Sunohara, Matthew","first_name":"Matthew"}],"arxiv":1,"status":"public","type":"journal_article","ec_funded":1,"citation":{"apa":"Arroyo Guevara, A. M., Richter, R. B., & Sunohara, M. (2021). Extending drawings of complete graphs into arrangements of pseudocircles. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1313234","ista":"Arroyo Guevara AM, Richter RB, Sunohara M. 2021. Extending drawings of complete graphs into arrangements of pseudocircles. SIAM Journal on Discrete Mathematics. 35(2), 1050–1076.","chicago":"Arroyo Guevara, Alan M, R. Bruce Richter, and Matthew Sunohara. “Extending Drawings of Complete Graphs into Arrangements of Pseudocircles.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/20M1313234.","mla":"Arroyo Guevara, Alan M., et al. “Extending Drawings of Complete Graphs into Arrangements of Pseudocircles.” SIAM Journal on Discrete Mathematics, vol. 35, no. 2, Society for Industrial and Applied Mathematics, 2021, pp. 1050–76, doi:10.1137/20M1313234.","ama":"Arroyo Guevara AM, Richter RB, Sunohara M. Extending drawings of complete graphs into arrangements of pseudocircles. SIAM Journal on Discrete Mathematics. 2021;35(2):1050-1076. doi:10.1137/20M1313234","ieee":"A. M. Arroyo Guevara, R. B. Richter, and M. Sunohara, “Extending drawings of complete graphs into arrangements of pseudocircles,” SIAM Journal on Discrete Mathematics, vol. 35, no. 2. Society for Industrial and Applied Mathematics, pp. 1050–1076, 2021.","short":"A.M. Arroyo Guevara, R.B. Richter, M. Sunohara, SIAM Journal on Discrete Mathematics 35 (2021) 1050–1076."},"date_created":"2021-06-06T22:01:30Z","year":"2021","doi":"10.1137/20M1313234","article_type":"original","_id":"9468","external_id":{"isi":["000674142200022"],"arxiv":["2001.06053"]},"abstract":[{"text":"Motivated by the successful application of geometry to proving the Harary--Hill conjecture for “pseudolinear” drawings of $K_n$, we introduce “pseudospherical” drawings of graphs. A spherical drawing of a graph $G$ is a drawing in the unit sphere $\\mathbb{S}^2$ in which the vertices of $G$ are represented as points---no three on a great circle---and the edges of $G$ are shortest-arcs in $\\mathbb{S}^2$ connecting pairs of vertices. Such a drawing has three properties: (1) every edge $e$ is contained in a simple closed curve $\\gamma_e$ such that the only vertices in $\\gamma_e$ are the ends of $e$; (2) if $e\\ne f$, then $\\gamma_e\\cap\\gamma_f$ has precisely two crossings; and (3) if $e\\ne f$, then $e$ intersects $\\gamma_f$ at most once, in either a crossing or an end of $e$. We use properties (1)--(3) to define a pseudospherical drawing of $G$. Our main result is that for the complete graph, properties (1)--(3) are equivalent to the same three properties but with “precisely two crossings” in (2) replaced by “at most two crossings.” The proof requires a result in the geometric transversal theory of arrangements of pseudocircles. This is proved using the surprising result that the absence of special arcs (coherent spirals) in an arrangement of simple closed curves characterizes the fact that any two curves in the arrangement have at most two crossings. Our studies provide the necessary ideas for exhibiting a drawing of $K_{10}$ that has no extension to an arrangement of pseudocircles and a drawing of $K_9$ that does extend to an arrangement of pseudocircles, but no such extension has all pairs of pseudocircles crossing twice.\r\n","lang":"eng"}],"publication_status":"published","department":[{"_id":"UlWa"}],"page":"1050-1076","quality_controlled":"1","volume":35,"publisher":"Society for Industrial and Applied Mathematics","date_published":"2021-05-20T00:00:00Z","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}]},{"date_created":"2021-06-13T22:01:32Z","citation":{"apa":"Ivanov, G., & Tsiutsiurupa, I. (2021). Functional Löwner ellipsoids. Journal of Geometric Analysis. Springer. https://doi.org/10.1007/s12220-021-00691-4","ista":"Ivanov G, Tsiutsiurupa I. 2021. Functional Löwner ellipsoids. Journal of Geometric Analysis. 31, 11493–11528.","mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “Functional Löwner Ellipsoids.” Journal of Geometric Analysis, vol. 31, Springer, 2021, pp. 11493–528, doi:10.1007/s12220-021-00691-4.","chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “Functional Löwner Ellipsoids.” Journal of Geometric Analysis. Springer, 2021. https://doi.org/10.1007/s12220-021-00691-4.","short":"G. Ivanov, I. Tsiutsiurupa, Journal of Geometric Analysis 31 (2021) 11493–11528.","ama":"Ivanov G, Tsiutsiurupa I. Functional Löwner ellipsoids. Journal of Geometric Analysis. 2021;31:11493-11528. doi:10.1007/s12220-021-00691-4","ieee":"G. Ivanov and I. Tsiutsiurupa, “Functional Löwner ellipsoids,” Journal of Geometric Analysis, vol. 31. Springer, pp. 11493–11528, 2021."},"acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-2019-1926.","year":"2021","article_type":"original","_id":"9548","doi":"10.1007/s12220-021-00691-4","publication_status":"published","external_id":{"arxiv":["2008.09543"],"isi":["000656507500001"]},"abstract":[{"lang":"eng","text":"We extend the notion of the minimal volume ellipsoid containing a convex body in Rd to the setting of logarithmically concave functions. We consider a vast class of logarithmically concave functions whose superlevel sets are concentric ellipsoids. For a fixed function from this class, we consider the set of all its “affine” positions. For any log-concave function f on Rd, we consider functions belonging to this set of “affine” positions, and find the one with the minimal integral under the condition that it is pointwise greater than or equal to f. We study the properties of existence and uniqueness of the solution to this problem. For any s∈[0,+∞), we consider the construction dual to the recently defined John s-function (Ivanov and Naszódi in Functional John ellipsoids. arXiv preprint: arXiv:2006.09934, 2020). We prove that such a construction determines a unique function and call it the Löwner s-function of f. We study the Löwner s-functions as s tends to zero and to infinity. Finally, extending the notion of the outer volume ratio, we define the outer integral ratio of a log-concave function and give an asymptotically tight bound on it."}],"department":[{"_id":"UlWa"}],"page":"11493-11528","volume":31,"quality_controlled":"1","publisher":"Springer","date_published":"2021-05-31T00:00:00Z","title":"Functional Löwner ellipsoids","date_updated":"2023-08-08T14:04:49Z","oa":1,"article_processing_charge":"No","scopus_import":"1","intvolume":" 31","isi":1,"language":[{"iso":"eng"}],"publication":"Journal of Geometric Analysis","author":[{"full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"full_name":"Tsiutsiurupa, Igor","first_name":"Igor","last_name":"Tsiutsiurupa"}],"arxiv":1,"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2008.09543","open_access":"1"}],"day":"31","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"05","publication_identifier":{"issn":["1050-6926"],"eissn":["1559-002X"]},"type":"journal_article","status":"public"},{"_id":"10856","article_type":"original","file_date_updated":"2022-03-18T09:31:59Z","doi":"10.1515/agms-2020-0103","keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"citation":{"apa":"Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103","ieee":"G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.","ama":"Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18.","chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103.","mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:10.1515/agms-2020-0103.","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18."},"date_created":"2022-03-18T09:25:14Z","year":"2021","acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer for valuable remarks.","volume":9,"quality_controlled":"1","page":"1-18","department":[{"_id":"UlWa"}],"date_published":"2021-01-29T00:00:00Z","publisher":"De Gruyter","publication_status":"published","abstract":[{"text":"We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.","lang":"eng"}],"external_id":{"arxiv":["2004.02674"],"isi":["000734286800001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"language":[{"iso":"eng"}],"publication":"Analysis and Geometry in Metric Spaces","title":"On the volume of sections of the cube","article_processing_charge":"No","issue":"1","oa":1,"date_updated":"2023-08-17T07:07:58Z","has_accepted_license":"1","intvolume":" 9","scopus_import":"1","isi":1,"type":"journal_article","status":"public","arxiv":1,"author":[{"full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"last_name":"Tsiutsiurupa","first_name":"Igor","full_name":"Tsiutsiurupa, Igor"}],"file":[{"creator":"dernst","content_type":"application/pdf","file_size":789801,"relation":"main_file","access_level":"open_access","file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","file_id":"10857","checksum":"7e615ac8489f5eae580b6517debfdc53","success":1,"date_updated":"2022-03-18T09:31:59Z","date_created":"2022-03-18T09:31:59Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"29","oa_version":"Published Version","month":"01","publication_identifier":{"issn":["2299-3274"]}},{"year":"2021","acknowledgement":"The author was supported by the Swiss National Science Foundation grant 200021_179133. The author acknowledges the financial support from the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no. 075-15-2019-1926.","keyword":["General Mathematics","Tight frame","Grassmannian","zonotope"],"date_created":"2022-03-18T09:55:59Z","citation":{"apa":"Ivanov, G. (2021). Tight frames and related geometric problems. Canadian Mathematical Bulletin. Canadian Mathematical Society. https://doi.org/10.4153/s000843952000096x","chicago":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin. Canadian Mathematical Society, 2021. https://doi.org/10.4153/s000843952000096x.","mla":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin, vol. 64, no. 4, Canadian Mathematical Society, 2021, pp. 942–63, doi:10.4153/s000843952000096x.","ista":"Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 64(4), 942–963.","short":"G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963.","ama":"Ivanov G. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 2021;64(4):942-963. doi:10.4153/s000843952000096x","ieee":"G. Ivanov, “Tight frames and related geometric problems,” Canadian Mathematical Bulletin, vol. 64, no. 4. Canadian Mathematical Society, pp. 942–963, 2021."},"doi":"10.4153/s000843952000096x","_id":"10860","article_type":"original","abstract":[{"lang":"eng","text":"A tight frame is the orthogonal projection of some orthonormal basis of Rn onto Rk. We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes."}],"external_id":{"arxiv":["1804.10055"],"isi":["000730165300021"]},"publication_status":"published","date_published":"2021-12-18T00:00:00Z","publisher":"Canadian Mathematical Society","volume":64,"quality_controlled":"1","department":[{"_id":"UlWa"}],"page":"942-963","isi":1,"scopus_import":"1","intvolume":" 64","article_processing_charge":"No","issue":"4","oa":1,"date_updated":"2023-09-05T12:43:09Z","title":"Tight frames and related geometric problems","publication":"Canadian Mathematical Bulletin","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0008-4395"],"eissn":["1496-4287"]},"month":"12","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"18","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.10055"}],"arxiv":1,"author":[{"full_name":"Ivanov, Grigory","first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov"}],"type":"journal_article","status":"public"},{"title":"Inserting one edge into a simple drawing is hard","date_updated":"2023-09-05T15:09:16Z","article_processing_charge":"No","scopus_import":"1","intvolume":" 12301","language":[{"iso":"eng"}],"publication":"Graph-Theoretic Concepts in Computer Science","author":[{"last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M"},{"last_name":"Klute","first_name":"Fabian","full_name":"Klute, Fabian"},{"last_name":"Parada","full_name":"Parada, Irene","first_name":"Irene"},{"last_name":"Seidel","full_name":"Seidel, Raimund","first_name":"Raimund"},{"full_name":"Vogtenhuber, Birgit","first_name":"Birgit","last_name":"Vogtenhuber"},{"full_name":"Wiedera, Tilo","first_name":"Tilo","last_name":"Wiedera"}],"day":"09","oa_version":"None","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","conference":{"location":"Leeds, United Kingdom","end_date":"2020-06-26","name":"WG: Workshop on Graph-Theoretic Concepts in Computer Science","start_date":"2020-06-24"},"month":"10","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030604394","9783030604400"],"issn":["0302-9743"]},"alternative_title":["LNCS"],"status":"public","type":"conference","date_created":"2020-11-06T08:45:03Z","citation":{"apa":"Arroyo Guevara, A. M., Klute, F., Parada, I., Seidel, R., Vogtenhuber, B., & Wiedera, T. (2020). Inserting one edge into a simple drawing is hard. In Graph-Theoretic Concepts in Computer Science (Vol. 12301, pp. 325–338). Leeds, United Kingdom: Springer Nature. https://doi.org/10.1007/978-3-030-60440-0_26","short":"A.M. Arroyo Guevara, F. Klute, I. Parada, R. Seidel, B. Vogtenhuber, T. Wiedera, in:, Graph-Theoretic Concepts in Computer Science, Springer Nature, 2020, pp. 325–338.","ieee":"A. M. Arroyo Guevara, F. Klute, I. Parada, R. Seidel, B. Vogtenhuber, and T. Wiedera, “Inserting one edge into a simple drawing is hard,” in Graph-Theoretic Concepts in Computer Science, Leeds, United Kingdom, 2020, vol. 12301, pp. 325–338.","ama":"Arroyo Guevara AM, Klute F, Parada I, Seidel R, Vogtenhuber B, Wiedera T. Inserting one edge into a simple drawing is hard. In: Graph-Theoretic Concepts in Computer Science. Vol 12301. Springer Nature; 2020:325-338. doi:10.1007/978-3-030-60440-0_26","mla":"Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is Hard.” Graph-Theoretic Concepts in Computer Science, vol. 12301, Springer Nature, 2020, pp. 325–38, doi:10.1007/978-3-030-60440-0_26.","ista":"Arroyo Guevara AM, Klute F, Parada I, Seidel R, Vogtenhuber B, Wiedera T. 2020. Inserting one edge into a simple drawing is hard. Graph-Theoretic Concepts in Computer Science. WG: Workshop on Graph-Theoretic Concepts in Computer Science, LNCS, vol. 12301, 325–338.","chicago":"Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Raimund Seidel, Birgit Vogtenhuber, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is Hard.” In Graph-Theoretic Concepts in Computer Science, 12301:325–38. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-60440-0_26."},"year":"2020","ec_funded":1,"_id":"8732","doi":"10.1007/978-3-030-60440-0_26","publication_status":"published","abstract":[{"text":"A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP -complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ , it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.","lang":"eng"}],"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"page":"325-338","department":[{"_id":"UlWa"}],"quality_controlled":"1","volume":12301,"publisher":"Springer Nature","date_published":"2020-10-09T00:00:00Z"},{"oa":1,"date_updated":"2023-08-14T11:43:54Z","issue":"6","article_processing_charge":"No","title":"Eliminating higher-multiplicity intersections, III. Codimension 2","isi":1,"scopus_import":"1","intvolume":" 75","language":[{"iso":"eng"}],"publication":"Russian Mathematical Surveys","author":[{"full_name":"Avvakumov, Sergey","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"},{"id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","last_name":"Mabillard","first_name":"Isaac","full_name":"Mabillard, Isaac"},{"full_name":"Skopenkov, A. B.","first_name":"A. B.","last_name":"Skopenkov"}],"arxiv":1,"publication_identifier":{"issn":["0036-0279"]},"month":"12","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.03501"}],"day":"01","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","type":"journal_article","acknowledgement":"This research was carried out with the support of the Russian Foundation for Basic Research(grant no. 19-01-00169)","year":"2020","date_created":"2021-04-04T22:01:22Z","citation":{"chicago":"Avvakumov, Sergey, Uli Wagner, Isaac Mabillard, and A. B. Skopenkov. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” Russian Mathematical Surveys. IOP Publishing, 2020. https://doi.org/10.1070/RM9943.","mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” Russian Mathematical Surveys, vol. 75, no. 6, IOP Publishing, 2020, pp. 1156–58, doi:10.1070/RM9943.","ista":"Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. 2020. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 75(6), 1156–1158.","ieee":"S. Avvakumov, U. Wagner, I. Mabillard, and A. B. Skopenkov, “Eliminating higher-multiplicity intersections, III. Codimension 2,” Russian Mathematical Surveys, vol. 75, no. 6. IOP Publishing, pp. 1156–1158, 2020.","ama":"Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 2020;75(6):1156-1158. doi:10.1070/RM9943","short":"S. Avvakumov, U. Wagner, I. Mabillard, A.B. Skopenkov, Russian Mathematical Surveys 75 (2020) 1156–1158.","apa":"Avvakumov, S., Wagner, U., Mabillard, I., & Skopenkov, A. B. (2020). Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM9943"},"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"8183"},{"relation":"later_version","id":"10220","status":"public"}]},"_id":"9308","article_type":"original","doi":"10.1070/RM9943","publication_status":"published","external_id":{"isi":["000625983100001"],"arxiv":["1511.03501"]},"publisher":"IOP Publishing","date_published":"2020-12-01T00:00:00Z","page":"1156-1158","department":[{"_id":"UlWa"}],"quality_controlled":"1","volume":75},{"year":"2020","date_created":"2020-05-10T22:00:48Z","citation":{"chicago":"Filakovský, Marek, Uli Wagner, and Stephan Y Zhechev. “Embeddability of Simplicial Complexes Is Undecidable.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2020–January:767–85. SIAM, 2020. https://doi.org/10.1137/1.9781611975994.47.","ista":"Filakovský M, Wagner U, Zhechev SY. 2020. Embeddability of simplicial complexes is undecidable. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2020–January, 767–785.","mla":"Filakovský, Marek, et al. “Embeddability of Simplicial Complexes Is Undecidable.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020–January, SIAM, 2020, pp. 767–85, doi:10.1137/1.9781611975994.47.","short":"M. Filakovský, U. Wagner, S.Y. Zhechev, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 767–785.","ama":"Filakovský M, Wagner U, Zhechev SY. Embeddability of simplicial complexes is undecidable. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 2020-January. SIAM; 2020:767-785. doi:10.1137/1.9781611975994.47","ieee":"M. Filakovský, U. Wagner, and S. Y. Zhechev, “Embeddability of simplicial complexes is undecidable,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Salt Lake City, UT, United States, 2020, vol. 2020–January, pp. 767–785.","apa":"Filakovský, M., Wagner, U., & Zhechev, S. Y. (2020). Embeddability of simplicial complexes is undecidable. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2020–January, pp. 767–785). Salt Lake City, UT, United States: SIAM. https://doi.org/10.1137/1.9781611975994.47"},"_id":"7806","doi":"10.1137/1.9781611975994.47","publication_status":"published","abstract":[{"text":"We consider the following decision problem EMBEDk→d in computational topology (where k ≤ d are fixed positive integers): Given a finite simplicial complex K of dimension k, does there exist a (piecewise-linear) embedding of K into ℝd?\r\nThe special case EMBED1→2 is graph planarity, which is decidable in linear time, as shown by Hopcroft and Tarjan. In higher dimensions, EMBED2→3 and EMBED3→3 are known to be decidable (as well as NP-hard), and recent results of Čadek et al. in computational homotopy theory, in combination with the classical Haefliger–Weber theorem in geometric topology, imply that EMBEDk→d can be solved in polynomial time for any fixed pair (k, d) of dimensions in the so-called metastable range .\r\nHere, by contrast, we prove that EMBEDk→d is algorithmically undecidable for almost all pairs of dimensions outside the metastable range, namely for . This almost completely resolves the decidability vs. undecidability of EMBEDk→d in higher dimensions and establishes a sharp dichotomy between polynomial-time solvability and undecidability.\r\nOur result complements (and in a wide range of dimensions strengthens) earlier results of Matoušek, Tancer, and the second author, who showed that EMBEDk→d is undecidable for 4 ≤ k ϵ {d – 1, d}, and NP-hard for all remaining pairs (k, d) outside the metastable range and satisfying d ≥ 4.","lang":"eng"}],"project":[{"_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF"}],"date_published":"2020-01-01T00:00:00Z","publisher":"SIAM","volume":"2020-January","quality_controlled":"1","page":"767-785","department":[{"_id":"UlWa"}],"article_processing_charge":"No","oa":1,"date_updated":"2021-01-12T08:15:38Z","title":"Embeddability of simplicial complexes is undecidable","scopus_import":1,"language":[{"iso":"eng"}],"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","author":[{"full_name":"Filakovský, Marek","first_name":"Marek","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","last_name":"Filakovský"},{"full_name":"Wagner, Uli","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"},{"first_name":"Stephan Y","full_name":"Zhechev, Stephan Y","last_name":"Zhechev","id":"3AA52972-F248-11E8-B48F-1D18A9856A87"}],"publication_identifier":{"isbn":["9781611975994"]},"month":"01","conference":{"location":"Salt Lake City, UT, United States","end_date":"2020-01-08","name":"SODA: Symposium on Discrete Algorithms","start_date":"2020-01-05"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"01","main_file_link":[{"url":"https://doi.org/10.1137/1.9781611975994.47","open_access":"1"}],"type":"conference","status":"public"},{"related_material":{"record":[{"status":"public","id":"12129","relation":"later_version"}]},"date_created":"2020-05-10T22:00:48Z","citation":{"apa":"Wagner, U., & Welzl, E. (2020). Connectivity of triangulation flip graphs in the plane (Part I: Edge flips). In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2020–January, pp. 2823–2841). Salt Lake City, UT, United States: SIAM. https://doi.org/10.1137/1.9781611975994.172","short":"U. Wagner, E. Welzl, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 2823–2841.","ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane (Part I: Edge flips),” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Salt Lake City, UT, United States, 2020, vol. 2020–January, pp. 2823–2841.","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane (Part I: Edge flips). In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 2020-January. SIAM; 2020:2823-2841. doi:10.1137/1.9781611975994.172","mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part I: Edge Flips).” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020–January, SIAM, 2020, pp. 2823–41, doi:10.1137/1.9781611975994.172.","ista":"Wagner U, Welzl E. 2020. Connectivity of triangulation flip graphs in the plane (Part I: Edge flips). Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2020–January, 2823–2841.","chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part I: Edge Flips).” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2020–January:2823–41. SIAM, 2020. https://doi.org/10.1137/1.9781611975994.172."},"year":"2020","doi":"10.1137/1.9781611975994.172","_id":"7807","abstract":[{"text":"In a straight-line embedded triangulation of a point set P in the plane, removing an inner edge and—provided the resulting quadrilateral is convex—adding the other diagonal is called an edge flip. The (edge) flip graph has all triangulations as vertices, and a pair of triangulations is adjacent if they can be obtained from each other by an edge flip. The goal of this paper is to contribute to a better understanding of the flip graph, with an emphasis on its connectivity.\r\nFor sets in general position, it is known that every triangulation allows at least edge flips (a tight bound) which gives the minimum degree of any flip graph for n points. We show that for every point set P in general position, the flip graph is at least -vertex connected. Somewhat more strongly, we show that the vertex connectivity equals the minimum degree occurring in the flip graph, i.e. the minimum number of flippable edges in any triangulation of P, provided P is large enough. Finally, we exhibit some of the geometry of the flip graph by showing that the flip graph can be covered by 1-skeletons of polytopes of dimension (products of associahedra).\r\nA corresponding result ((n – 3)-vertex connectedness) can be shown for the bistellar flip graph of partial triangulations, i.e. the set of all triangulations of subsets of P which contain all extreme points of P. This will be treated separately in a second part.","lang":"eng"}],"external_id":{"arxiv":["2003.13557"]},"publication_status":"published","volume":"2020-January","quality_controlled":"1","page":"2823-2841","department":[{"_id":"UlWa"}],"date_published":"2020-01-01T00:00:00Z","publisher":"SIAM","scopus_import":1,"title":"Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)","article_processing_charge":"No","date_updated":"2023-08-04T08:51:07Z","oa":1,"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.1137/1.9781611975994.172","open_access":"1"}],"day":"01","oa_version":"Submitted Version","month":"01","publication_identifier":{"isbn":["9781611975994"]},"conference":{"start_date":"2020-01-05","name":"SODA: Symposium on Discrete Algorithms","end_date":"2020-01-08","location":"Salt Lake City, UT, United States"},"arxiv":1,"author":[{"orcid":"0000-0002-1494-0568","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli","first_name":"Uli"},{"first_name":"Emo","full_name":"Welzl, Emo","last_name":"Welzl"}],"type":"conference","status":"public"},{"alternative_title":["ISTA Thesis"],"type":"dissertation","status":"public","month":"06","publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-005-3"]},"oa_version":"Published Version","day":"09","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:34:00Z","file_name":"THESIS_Zuzka_Masarova.pdf","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","file_id":"7945","relation":"main_file","file_size":13661779,"access_level":"open_access","content_type":"application/pdf","creator":"zmasarov"},{"date_created":"2020-06-08T00:35:30Z","date_updated":"2020-07-14T12:48:05Z","file_id":"7946","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","checksum":"45341a35b8f5529c74010b7af43ac188","relation":"source_file","file_size":32184006,"access_level":"closed","content_type":"application/zip","creator":"zmasarov"}],"author":[{"last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","first_name":"Zuzana"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","date_updated":"2023-09-07T13:17:37Z","oa":1,"article_processing_charge":"No","title":"Reconfiguration problems","publisher":"Institute of Science and Technology Austria","license":"https://creativecommons.org/licenses/by-sa/4.0/","date_published":"2020-06-09T00:00:00Z","supervisor":[{"full_name":"Wagner, Uli","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"page":"160","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"ddc":["516","514"],"tmp":{"short":"CC BY-SA (4.0)","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","image":"/images/cc_by_sa.png"},"abstract":[{"text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.","lang":"eng"}],"publication_status":"published","doi":"10.15479/AT:ISTA:7944","file_date_updated":"2020-07-14T12:48:05Z","_id":"7944","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"7950"},{"relation":"part_of_dissertation","id":"5986","status":"public"}]},"degree_awarded":"PhD","year":"2020","citation":{"apa":"Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944."},"date_created":"2020-06-08T00:49:46Z","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"]}]