--- _id: '7960' abstract: - lang: eng text: Let A={A1,…,An} be a family of sets in the plane. For 0≤i2b be integers. We prove that if each k-wise or (k+1)-wise intersection of sets from A has at most b path-connected components, which all are open, then fk+1=0 implies fk≤cfk−1 for some positive constant c depending only on b and k. These results also extend to two-dimensional compact surfaces. acknowledgement: "We are very grateful to Pavel Paták for many helpful discussions and remarks. We also thank the referees for helpful comments, which greatly improved the presentation.\r\nThe project was supported by ERC Advanced Grant 320924. GK was also partially supported by NSF grant DMS1300120. The research stay of ZP at IST Austria is funded by the project CZ.02.2.69/0.0/0.0/17_050/0008466 Improvement of internationalization in the field of research and development at Charles University, through the support of quality projects MSCA-IF." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Gil full_name: Kalai, Gil last_name: Kalai - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 citation: ama: Kalai G, Patakova Z. Intersection patterns of planar sets. Discrete and Computational Geometry. 2020;64:304-323. doi:10.1007/s00454-020-00205-z apa: Kalai, G., & Patakova, Z. (2020). Intersection patterns of planar sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00205-z chicago: Kalai, Gil, and Zuzana Patakova. “Intersection Patterns of Planar Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00205-z. ieee: G. Kalai and Z. Patakova, “Intersection patterns of planar sets,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 304–323, 2020. ista: Kalai G, Patakova Z. 2020. Intersection patterns of planar sets. Discrete and Computational Geometry. 64, 304–323. mla: Kalai, Gil, and Zuzana Patakova. “Intersection Patterns of Planar Sets.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 304–23, doi:10.1007/s00454-020-00205-z. short: G. Kalai, Z. Patakova, Discrete and Computational Geometry 64 (2020) 304–323. date_created: 2020-06-14T22:00:50Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-08-21T08:26:34Z day: '01' department: - _id: UlWa doi: 10.1007/s00454-020-00205-z external_id: arxiv: - '1907.00885' isi: - '000537329400001' intvolume: ' 64' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1907.00885 month: '09' oa: 1 oa_version: Preprint page: 304-323 publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Intersection patterns of planar sets type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 64 year: '2020' ... --- _id: '7989' abstract: - lang: eng text: 'We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.' alternative_title: - LIPIcs article_number: 61:1-61:13 article_processing_charge: No arxiv: 1 author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 citation: ama: 'Patakova Z. Bounding radon number via Betti numbers. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.61' apa: 'Patakova, Z. (2020). Bounding radon number via Betti numbers. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.61' chicago: Patakova, Zuzana. “Bounding Radon Number via Betti Numbers.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.61. ieee: Z. Patakova, “Bounding radon number via Betti numbers,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Patakova Z. 2020. Bounding radon number via Betti numbers. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 61:1-61:13.' mla: Patakova, Zuzana. “Bounding Radon Number via Betti Numbers.” 36th International Symposium on Computational Geometry, vol. 164, 61:1-61:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.61. short: Z. Patakova, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:18Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:22Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.61 external_id: arxiv: - '1908.01677' file: - access_level: open_access checksum: d0996ca5f6eb32ce955ce782b4f2afbe content_type: application/pdf creator: dernst date_created: 2020-06-23T06:56:23Z date_updated: 2020-07-14T12:48:06Z file_id: '8005' file_name: 2020_LIPIcsSoCG_Patakova_61.pdf file_size: 645421 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Bounding radon number via Betti numbers tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7990' abstract: - lang: eng text: 'Given a finite point set P in general position in the plane, a full triangulation is a maximal straight-line embedded plane graph on P. A partial triangulation on 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, 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 goal of this paper is to investigate the structure of this graph, with emphasis on its connectivity. For sets P of n points in general position, we show that the bistellar flip graph is (n-3)-connected, thereby answering, for sets in general position, an open questions raised in a book (by De Loera, Rambau, and Santos) and a survey (by Lee and Santos) on triangulations. This matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points and projecting the lower convex hull), where (n-3)-connectivity has been known since the late 1980s through the secondary polytope (Gelfand, Kapranov, Zelevinsky) and Balinski’s Theorem. Our methods also yield the following results (see the full version [Wagner and Welzl, 2020]): (i) 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 are regular iff the trivial subdivision has height n-3 in the partial order of partial subdivisions. (iv) There are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction).' alternative_title: - LIPIcs article_number: 67:1 - 67:16 article_processing_charge: No arxiv: 1 author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Emo full_name: Welzl, Emo last_name: Welzl citation: ama: 'Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips). In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.67' apa: 'Wagner, U., & Welzl, E. (2020). Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips). In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.67' chicago: 'Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part II: Bistellar Flips).” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.67.' ieee: 'U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips),” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.' ista: 'Wagner U, Welzl E. 2020. Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips). 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 67:1-67:16.' mla: 'Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part II: Bistellar Flips).” 36th International Symposium on Computational Geometry, vol. 164, 67:1-67:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.67.' short: U. Wagner, E. Welzl, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:19Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-08-04T08:51:07Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.67 external_id: arxiv: - '2003.13557' file: - access_level: open_access checksum: 3f6925be5f3dcdb3b14cab92f410edf7 content_type: application/pdf creator: dernst date_created: 2020-06-23T06:37:27Z date_updated: 2020-07-14T12:48:06Z file_id: '8003' file_name: 2020_LIPIcsSoCG_Wagner.pdf file_size: 793187 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '12129' relation: later_version status: public scopus_import: 1 status: public title: 'Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7991' abstract: - lang: eng text: 'We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.' alternative_title: - LIPIcs article_number: 12:1 - 12:15 article_processing_charge: No arxiv: 1 author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Gabriel full_name: Nivasch, Gabriel last_name: Nivasch citation: ama: 'Avvakumov S, Nivasch G. Homotopic curve shortening and the affine curve-shortening flow. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.12' apa: 'Avvakumov, S., & Nivasch, G. (2020). Homotopic curve shortening and the affine curve-shortening flow. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.12' chicago: Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.12. ieee: S. Avvakumov and G. Nivasch, “Homotopic curve shortening and the affine curve-shortening flow,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Avvakumov S, Nivasch G. 2020. Homotopic curve shortening and the affine curve-shortening flow. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 12:1-12:15.' mla: Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” 36th International Symposium on Computational Geometry, vol. 164, 12:1-12:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.12. short: S. Avvakumov, G. Nivasch, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:19Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:23Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.12 external_id: arxiv: - '1909.00263' file: - access_level: open_access checksum: 6872df6549142f709fb6354a1b2f2c06 content_type: application/pdf creator: dernst date_created: 2020-06-23T11:13:49Z date_updated: 2020-07-14T12:48:06Z file_id: '8007' file_name: 2020_LIPIcsSoCG_Avvakumov.pdf file_size: 575896 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '06' oa: 1 oa_version: Published Version project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Homotopic curve shortening and the affine curve-shortening flow tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7992' abstract: - lang: eng text: 'Let K be a convex body in ℝⁿ (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K ∩ h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p₀ is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n ≥ 2, there are always at least three distinct barycentric cuts through the point p₀ ∈ K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p₀ are guaranteed if n ≥ 3.' alternative_title: - LIPIcs article_number: 62:1 - 62:16 article_processing_charge: No arxiv: 1 author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.62' apa: 'Patakova, Z., Tancer, M., & Wagner, U. (2020). Barycentric cuts through a convex body. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.62' chicago: Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through a Convex Body.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.62. ieee: Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex body,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Patakova Z, Tancer M, Wagner U. 2020. Barycentric cuts through a convex body. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 62:1-62:16.' mla: Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” 36th International Symposium on Computational Geometry, vol. 164, 62:1-62:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.62. short: Z. Patakova, M. Tancer, U. Wagner, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:20Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:23Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.62 external_id: arxiv: - '2003.13536' file: - access_level: open_access checksum: ce1c9194139a664fb59d1efdfc88eaae content_type: application/pdf creator: dernst date_created: 2020-06-23T06:45:52Z date_updated: 2020-07-14T12:48:06Z file_id: '8004' file_name: 2020_LIPIcsSoCG_Patakova.pdf file_size: 750318 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Barycentric cuts through a convex body tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7994' abstract: - lang: eng text: In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible. alternative_title: - LIPIcs article_number: 9:1 - 9:14 article_processing_charge: No arxiv: 1 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 - first_name: Julien full_name: Bensmail, Julien last_name: Bensmail - first_name: R. full_name: Bruce Richter, R. last_name: Bruce Richter citation: ama: 'Arroyo Guevara AM, Bensmail J, Bruce Richter R. Extending drawings of graphs to arrangements of pseudolines. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.9' apa: 'Arroyo Guevara, A. M., Bensmail, J., & Bruce Richter, R. (2020). Extending drawings of graphs to arrangements of pseudolines. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.9' chicago: Arroyo Guevara, Alan M, Julien Bensmail, and R. Bruce Richter. “Extending Drawings of Graphs to Arrangements of Pseudolines.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.9. ieee: A. M. Arroyo Guevara, J. Bensmail, and R. Bruce Richter, “Extending drawings of graphs to arrangements of pseudolines,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Arroyo Guevara AM, Bensmail J, Bruce Richter R. 2020. Extending drawings of graphs to arrangements of pseudolines. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 9:1-9:14.' mla: Arroyo Guevara, Alan M., et al. “Extending Drawings of Graphs to Arrangements of Pseudolines.” 36th International Symposium on Computational Geometry, vol. 164, 9:1-9:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.9. short: A.M. Arroyo Guevara, J. Bensmail, R. Bruce Richter, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:21Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-02-23T13:22:12Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.9 ec_funded: 1 external_id: arxiv: - '1804.09317' file: - access_level: open_access checksum: 93571b76cf97d5b7c8aabaeaa694dd7e content_type: application/pdf creator: dernst date_created: 2020-06-23T11:06:23Z date_updated: 2020-07-14T12:48:06Z file_id: '8006' file_name: 2020_LIPIcsSoCG_Arroyo.pdf file_size: 592661 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Extending drawings of graphs to arrangements of pseudolines tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '8032' abstract: - lang: eng text: "Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”\r\nIn this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus." acknowledged_ssus: - _id: E-Lib - _id: CampIT alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Kristóf full_name: Huszár, Kristóf id: 33C26278-F248-11E8-B48F-1D18A9856A87 last_name: Huszár orcid: 0000-0002-5445-5057 citation: ama: Huszár K. Combinatorial width parameters for 3-dimensional manifolds. 2020. doi:10.15479/AT:ISTA:8032 apa: Huszár, K. (2020). Combinatorial width parameters for 3-dimensional manifolds. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:8032 chicago: Huszár, Kristóf. “Combinatorial Width Parameters for 3-Dimensional Manifolds.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:8032. ieee: K. Huszár, “Combinatorial width parameters for 3-dimensional manifolds,” Institute of Science and Technology Austria, 2020. ista: Huszár K. 2020. Combinatorial width parameters for 3-dimensional manifolds. Institute of Science and Technology Austria. mla: Huszár, Kristóf. Combinatorial Width Parameters for 3-Dimensional Manifolds. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:8032. short: K. Huszár, Combinatorial Width Parameters for 3-Dimensional Manifolds, Institute of Science and Technology Austria, 2020. date_created: 2020-06-26T10:00:36Z date_published: 2020-06-26T00:00:00Z date_updated: 2023-09-07T13:18:27Z day: '26' ddc: - '514' degree_awarded: PhD department: - _id: UlWa doi: 10.15479/AT:ISTA:8032 file: - access_level: open_access checksum: bd8be6e4f1addc863dfcc0fad29ee9c3 content_type: application/pdf creator: khuszar date_created: 2020-06-26T10:03:58Z date_updated: 2020-07-14T12:48:08Z file_id: '8034' file_name: Kristof_Huszar-Thesis.pdf file_size: 2637562 relation: main_file - access_level: closed checksum: d5f8456202b32f4a77552ef47a2837d1 content_type: application/x-zip-compressed creator: khuszar date_created: 2020-06-26T10:10:06Z date_updated: 2020-07-14T12:48:08Z file_id: '8035' file_name: Kristof_Huszar-Thesis-source.zip file_size: 7163491 relation: source_file file_date_updated: 2020-07-14T12:48:08Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: xviii+120 publication_identifier: isbn: - 978-3-99078-006-0 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '6556' relation: dissertation_contains status: public - id: '7093' relation: dissertation_contains status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer title: Combinatorial width parameters for 3-dimensional manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '8156' abstract: - lang: eng text: 'We present solutions to several problems originating from geometry and discrete mathematics: existence of equipartitions, maps without Tverberg multiple points, and inscribing quadrilaterals. Equivariant obstruction theory is the natural topological approach to these type of questions. However, for the specific problems we consider it had yielded only partial or no results. We get our results by complementing equivariant obstruction theory with other techniques from topology and geometry.' alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov citation: ama: Avvakumov S. Topological methods in geometry and discrete mathematics. 2020. doi:10.15479/AT:ISTA:8156 apa: Avvakumov, S. (2020). Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:8156 chicago: Avvakumov, Sergey. “Topological Methods in Geometry and Discrete Mathematics.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:8156. ieee: S. Avvakumov, “Topological methods in geometry and discrete mathematics,” Institute of Science and Technology Austria, 2020. ista: Avvakumov S. 2020. Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria. mla: Avvakumov, Sergey. Topological Methods in Geometry and Discrete Mathematics. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:8156. short: S. Avvakumov, Topological Methods in Geometry and Discrete Mathematics, Institute of Science and Technology Austria, 2020. date_created: 2020-07-23T09:51:29Z date_published: 2020-07-24T00:00:00Z date_updated: 2023-12-18T10:51:01Z day: '24' ddc: - '514' degree_awarded: PhD department: - _id: UlWa doi: 10.15479/AT:ISTA:8156 file: - access_level: closed content_type: application/zip creator: savvakum date_created: 2020-07-27T12:44:51Z date_updated: 2020-07-27T12:44:51Z file_id: '8178' file_name: source.zip file_size: 1061740 relation: source_file - access_level: open_access content_type: application/pdf creator: savvakum date_created: 2020-07-27T12:46:53Z date_updated: 2020-07-27T12:46:53Z file_id: '8179' file_name: thesis_pdfa.pdf file_size: 1336501 relation: main_file success: 1 file_date_updated: 2020-07-27T12:46:53Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '119' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '8182' relation: part_of_dissertation status: public - id: '8183' relation: part_of_dissertation status: public - id: '8185' relation: part_of_dissertation status: public - id: '8184' relation: part_of_dissertation status: public - id: '6355' relation: part_of_dissertation status: public - id: '75' relation: part_of_dissertation status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 title: Topological methods in geometry and discrete mathematics type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '15082' abstract: - lang: eng text: "Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2.\r\nWe show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter\r\nof this graph is either 4 or 5, independent of n." acknowledgement: Research on this work was initiated at the 6th Austrian-Japanese-Mexican-Spanish Workshop on Discrete Geometry and continued during the 16th European Geometric Graph-Week, both held near Strobl, Austria. We are grateful to the participants for the inspiring atmosphere. We especially thank Alexander Pilz for bringing this class of problems to our attention and Birgit Vogtenhuber for inspiring discussions. D.P. is partially supported by the FWF grant I 3340-N35 (Collaborative DACH project Arrangements and Drawings). The research stay of P.P. at IST Austria is funded by the project CZ.02.2.69/0.0/0.0/17_050/0008466 Improvement of internationalization in the field of research and development at Charles University, through the support of quality projects MSCA-IF. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922. article_number: '56' article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Julia full_name: Obmann, Julia last_name: Obmann - first_name: Pavel full_name: Patak, Pavel id: B593B804-1035-11EA-B4F1-947645A5BB83 last_name: Patak - first_name: Daniel full_name: Perz, Daniel last_name: Perz - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 citation: ama: 'Aichholzer O, Obmann J, Patak P, Perz D, Tkadlec J. Disjoint tree-compatible plane perfect matchings. In: 36th European Workshop on Computational Geometry. ; 2020.' apa: Aichholzer, O., Obmann, J., Patak, P., Perz, D., & Tkadlec, J. (2020). Disjoint tree-compatible plane perfect matchings. In 36th European Workshop on Computational Geometry. Würzburg, Germany, Virtual. chicago: Aichholzer, Oswin, Julia Obmann, Pavel Patak, Daniel Perz, and Josef Tkadlec. “Disjoint Tree-Compatible Plane Perfect Matchings.” In 36th European Workshop on Computational Geometry, 2020. ieee: O. Aichholzer, J. Obmann, P. Patak, D. Perz, and J. Tkadlec, “Disjoint tree-compatible plane perfect matchings,” in 36th European Workshop on Computational Geometry, Würzburg, Germany, Virtual, 2020. ista: 'Aichholzer O, Obmann J, Patak P, Perz D, Tkadlec J. 2020. Disjoint tree-compatible plane perfect matchings. 36th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 56.' mla: Aichholzer, Oswin, et al. “Disjoint Tree-Compatible Plane Perfect Matchings.” 36th European Workshop on Computational Geometry, 56, 2020. short: O. Aichholzer, J. Obmann, P. Patak, D. Perz, J. Tkadlec, in:, 36th European Workshop on Computational Geometry, 2020. conference: end_date: 2020-03-18 location: Würzburg, Germany, Virtual name: 'EuroCG: European Workshop on Computational Geometry' start_date: 2020-03-16 date_created: 2024-03-05T08:57:17Z date_published: 2020-04-01T00:00:00Z date_updated: 2024-03-05T09:00:07Z day: '01' department: - _id: KrCh - _id: UlWa language: - iso: eng main_file_link: - open_access: '1' url: https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/data/uploads/papers/eurocg20_paper_56.pdf month: '04' oa: 1 oa_version: Published Version publication: 36th European Workshop on Computational Geometry publication_status: published quality_controlled: '1' status: public title: Disjoint tree-compatible plane perfect matchings type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2020' ... --- _id: '6563' abstract: - lang: eng text: "This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps \U0001D453,\U0001D454:\U0001D44B→\U0001D44C, and the second computes the group [\U0001D6F4\U0001D44B,\U0001D44C]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to \U0001D434⊆\U0001D44B." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Marek full_name: Filakovský, Marek id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87 last_name: Filakovský - first_name: Lukas full_name: Vokřínek, Lukas last_name: Vokřínek citation: ama: Filakovský M, Vokřínek L. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 2020;20:311-330. doi:10.1007/s10208-019-09419-x apa: Filakovský, M., & Vokřínek, L. (2020). Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-019-09419-x chicago: Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic Viewpoint.” Foundations of Computational Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s10208-019-09419-x. ieee: M. Filakovský and L. Vokřínek, “Are two given maps homotopic? An algorithmic viewpoint,” Foundations of Computational Mathematics, vol. 20. Springer Nature, pp. 311–330, 2020. ista: Filakovský M, Vokřínek L. 2020. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 20, 311–330. mla: Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic Viewpoint.” Foundations of Computational Mathematics, vol. 20, Springer Nature, 2020, pp. 311–30, doi:10.1007/s10208-019-09419-x. short: M. Filakovský, L. Vokřínek, Foundations of Computational Mathematics 20 (2020) 311–330. date_created: 2019-06-16T21:59:14Z date_published: 2020-04-01T00:00:00Z date_updated: 2023-08-17T13:50:44Z day: '01' department: - _id: UlWa doi: 10.1007/s10208-019-09419-x external_id: arxiv: - '1312.2337' isi: - '000522437400004' intvolume: ' 20' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1312.2337 month: '04' oa: 1 oa_version: Preprint page: 311-330 project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: Foundations of Computational Mathematics publication_identifier: eissn: - '16153383' issn: - '16153375' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Are two given maps homotopic? An algorithmic viewpoint type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 20 year: '2020' ... --- _id: '6982' abstract: - lang: eng text: "We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ϕ : G → M of a graph G into a 2-manifold M maps the vertices in V(G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to the same point or overlapping arcs due to data compression or low resolution. This raises the computational problem of deciding whether a given map ϕ : G → M comes from an embedding. A map ϕ : G → M is a weak embedding if it can be perturbed into an embedding ψ ϵ : G → M with ‖ ϕ − ψ ϵ ‖ < ϵ for every ϵ > 0, where ‖.‖ is the unform norm.\r\nA polynomial-time algorithm for recognizing weak embeddings has recently been found by Fulek and Kynčl. It reduces the problem to solving a system of linear equations over Z2. It runs in O(n2ω)≤ O(n4.75) time, where ω ∈ [2,2.373) is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler: We perform a sequence of local operations that gradually “untangles” the image ϕ(G) into an embedding ψ(G) or reports that ϕ is not a weak embedding. It combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.\r\n" article_number: '50' article_type: original arxiv: 1 author: - first_name: Hugo full_name: Akitaya, Hugo last_name: Akitaya - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Csaba full_name: Tóth, Csaba last_name: Tóth citation: ama: Akitaya H, Fulek R, Tóth C. Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. 2019;15(4). doi:10.1145/3344549 apa: Akitaya, H., Fulek, R., & Tóth, C. (2019). Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. ACM. https://doi.org/10.1145/3344549 chicago: Akitaya, Hugo, Radoslav Fulek, and Csaba Tóth. “Recognizing Weak Embeddings of Graphs.” ACM Transactions on Algorithms. ACM, 2019. https://doi.org/10.1145/3344549. ieee: H. Akitaya, R. Fulek, and C. Tóth, “Recognizing weak embeddings of graphs,” ACM Transactions on Algorithms, vol. 15, no. 4. ACM, 2019. ista: Akitaya H, Fulek R, Tóth C. 2019. Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. 15(4), 50. mla: Akitaya, Hugo, et al. “Recognizing Weak Embeddings of Graphs.” ACM Transactions on Algorithms, vol. 15, no. 4, 50, ACM, 2019, doi:10.1145/3344549. short: H. Akitaya, R. Fulek, C. Tóth, ACM Transactions on Algorithms 15 (2019). date_created: 2019-11-04T15:45:17Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-09-15T12:19:31Z day: '01' department: - _id: UlWa doi: 10.1145/3344549 external_id: arxiv: - '1709.09209' intvolume: ' 15' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.09209 month: '10' oa: 1 oa_version: Preprint project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: ACM Transactions on Algorithms publication_status: published publisher: ACM quality_controlled: '1' related_material: record: - id: '309' relation: earlier_version status: public scopus_import: 1 status: public title: Recognizing weak embeddings of graphs type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2019' ... --- _id: '7034' abstract: - lang: eng text: We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani–Tutte theorem cannot be extended to the orientable surface of genus 4. As a base step in the construction we use a counterexample to an extension of the unified Hanani–Tutte theorem on the torus. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Jan full_name: Kynčl, Jan last_name: Kynčl citation: ama: Fulek R, Kynčl J. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 2019;39(6):1267-1279. doi:10.1007/s00493-019-3905-7 apa: Fulek, R., & Kynčl, J. (2019). Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-019-3905-7 chicago: Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica. Springer Nature, 2019. https://doi.org/10.1007/s00493-019-3905-7. ieee: R. Fulek and J. Kynčl, “Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4,” Combinatorica, vol. 39, no. 6. Springer Nature, pp. 1267–1279, 2019. ista: Fulek R, Kynčl J. 2019. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 39(6), 1267–1279. mla: Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica, vol. 39, no. 6, Springer Nature, 2019, pp. 1267–79, doi:10.1007/s00493-019-3905-7. short: R. Fulek, J. Kynčl, Combinatorica 39 (2019) 1267–1279. date_created: 2019-11-18T14:29:50Z date_published: 2019-10-29T00:00:00Z date_updated: 2023-08-30T07:26:25Z day: '29' department: - _id: UlWa doi: 10.1007/s00493-019-3905-7 ec_funded: 1 external_id: arxiv: - '1709.00508' isi: - '000493267200003' intvolume: ' 39' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.00508 month: '10' oa: 1 oa_version: Preprint page: 1267-1279 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: Combinatorica publication_identifier: eissn: - 1439-6912 issn: - 0209-9683 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4 type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 39 year: '2019' ... --- _id: '7093' abstract: - lang: eng text: "In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how \"simple\" or \"thin\" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth.\r\nIn view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs).\r\nWe derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 18(k+1) (resp. 4(3k+1))." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Kristóf full_name: Huszár, Kristóf id: 33C26278-F248-11E8-B48F-1D18A9856A87 last_name: Huszár orcid: 0000-0002-5445-5057 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Huszár K, Spreer J, Wagner U. On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. 2019;10(2):70–98. doi:10.20382/JOGC.V10I2A5 apa: Huszár, K., Spreer, J., & Wagner, U. (2019). On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. Computational Geometry Laborartoy. https://doi.org/10.20382/JOGC.V10I2A5 chicago: Huszár, Kristóf, Jonathan Spreer, and Uli Wagner. “On the Treewidth of Triangulated 3-Manifolds.” Journal of Computational Geometry. Computational Geometry Laborartoy, 2019. https://doi.org/10.20382/JOGC.V10I2A5. ieee: K. Huszár, J. Spreer, and U. Wagner, “On the treewidth of triangulated 3-manifolds,” Journal of Computational Geometry, vol. 10, no. 2. Computational Geometry Laborartoy, pp. 70–98, 2019. ista: Huszár K, Spreer J, Wagner U. 2019. On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. 10(2), 70–98. mla: Huszár, Kristóf, et al. “On the Treewidth of Triangulated 3-Manifolds.” Journal of Computational Geometry, vol. 10, no. 2, Computational Geometry Laborartoy, 2019, pp. 70–98, doi:10.20382/JOGC.V10I2A5. short: K. Huszár, J. Spreer, U. Wagner, Journal of Computational Geometry 10 (2019) 70–98. date_created: 2019-11-23T12:14:09Z date_published: 2019-11-01T00:00:00Z date_updated: 2023-09-07T13:18:26Z day: '01' ddc: - '514' department: - _id: UlWa doi: 10.20382/JOGC.V10I2A5 external_id: arxiv: - '1712.00434' file: - access_level: open_access checksum: c872d590d38d538404782bca20c4c3f5 content_type: application/pdf creator: khuszar date_created: 2019-11-23T12:35:16Z date_updated: 2020-07-14T12:47:49Z file_id: '7094' file_name: 479-1917-1-PB.pdf file_size: 857590 relation: main_file file_date_updated: 2020-07-14T12:47:49Z has_accepted_license: '1' intvolume: ' 10' issue: '2' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 70–98 publication: Journal of Computational Geometry publication_identifier: issn: - 1920-180X publication_status: published publisher: Computational Geometry Laborartoy quality_controlled: '1' related_material: record: - id: '285' relation: earlier_version status: public - id: '8032' relation: part_of_dissertation status: public status: public title: On the treewidth of triangulated 3-manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 10 year: '2019' ... --- _id: '7108' abstract: - lang: eng text: We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes. Another simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-shellable. article_number: '21' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Xavier full_name: Goaoc, Xavier last_name: Goaoc - first_name: Pavel full_name: Patak, Pavel id: B593B804-1035-11EA-B4F1-947645A5BB83 last_name: Patak - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin last_name: Tancer - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. Journal of the ACM. 2019;66(3). doi:10.1145/3314024 apa: Goaoc, X., Patak, P., Patakova, Z., Tancer, M., & Wagner, U. (2019). Shellability is NP-complete. Journal of the ACM. ACM. https://doi.org/10.1145/3314024 chicago: Goaoc, Xavier, Pavel Patak, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete.” Journal of the ACM. ACM, 2019. https://doi.org/10.1145/3314024. ieee: X. Goaoc, P. Patak, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” Journal of the ACM, vol. 66, no. 3. ACM, 2019. ista: Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. 2019. Shellability is NP-complete. Journal of the ACM. 66(3), 21. mla: Goaoc, Xavier, et al. “Shellability Is NP-Complete.” Journal of the ACM, vol. 66, no. 3, 21, ACM, 2019, doi:10.1145/3314024. short: X. Goaoc, P. Patak, Z. Patakova, M. Tancer, U. Wagner, Journal of the ACM 66 (2019). date_created: 2019-11-26T10:13:59Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-06T11:10:58Z day: '01' department: - _id: UlWa doi: 10.1145/3314024 external_id: arxiv: - '1711.08436' isi: - '000495406300007' intvolume: ' 66' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/pdf/1711.08436.pdf month: '06' oa: 1 oa_version: Preprint publication: Journal of the ACM publication_identifier: issn: - 0004-5411 publication_status: published publisher: ACM quality_controlled: '1' related_material: record: - id: '184' relation: earlier_version status: public scopus_import: '1' status: public title: Shellability is NP-complete type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 66 year: '2019' ... --- _id: '7230' abstract: - lang: eng text: Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing D(G) of a graph G by inserting a set of edges from the complement of G into D(G) such that the result is a simple drawing. In the context of rectilinear drawings, the problem is trivial. For pseudolinear drawings, the existence of such an extension follows from Levi’s enlargement lemma. In contrast, we prove that deciding if a given set of edges can be inserted into a simple drawing is NP-complete. Moreover, we show that the maximization version of the problem is APX-hard. We also present a polynomial-time algorithm for deciding whether one edge uv can be inserted into D(G) when {u,v} is a dominating set for the graph G. alternative_title: - LNCS article_processing_charge: No arxiv: 1 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 - first_name: Martin full_name: Derka, Martin last_name: Derka - first_name: Irene full_name: Parada, Irene last_name: Parada citation: ama: 'Arroyo Guevara AM, Derka M, Parada I. Extending simple drawings. In: 27th International Symposium on Graph Drawing and Network Visualization. Vol 11904. Springer Nature; 2019:230-243. doi:10.1007/978-3-030-35802-0_18' apa: 'Arroyo Guevara, A. M., Derka, M., & Parada, I. (2019). Extending simple drawings. In 27th International Symposium on Graph Drawing and Network Visualization (Vol. 11904, pp. 230–243). Prague, Czech Republic: Springer Nature. https://doi.org/10.1007/978-3-030-35802-0_18' chicago: Arroyo Guevara, Alan M, Martin Derka, and Irene Parada. “Extending Simple Drawings.” In 27th International Symposium on Graph Drawing and Network Visualization, 11904:230–43. Springer Nature, 2019. https://doi.org/10.1007/978-3-030-35802-0_18. ieee: A. M. Arroyo Guevara, M. Derka, and I. Parada, “Extending simple drawings,” in 27th International Symposium on Graph Drawing and Network Visualization, Prague, Czech Republic, 2019, vol. 11904, pp. 230–243. ista: 'Arroyo Guevara AM, Derka M, Parada I. 2019. Extending simple drawings. 27th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 11904, 230–243.' mla: Arroyo Guevara, Alan M., et al. “Extending Simple Drawings.” 27th International Symposium on Graph Drawing and Network Visualization, vol. 11904, Springer Nature, 2019, pp. 230–43, doi:10.1007/978-3-030-35802-0_18. short: A.M. Arroyo Guevara, M. Derka, I. Parada, in:, 27th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2019, pp. 230–243. conference: end_date: 2019-09-20 location: Prague, Czech Republic name: 'GD: Graph Drawing and Network Visualization' start_date: 2019-09-17 date_created: 2020-01-05T23:00:47Z date_published: 2019-11-28T00:00:00Z date_updated: 2023-09-06T14:56:00Z day: '28' department: - _id: UlWa doi: 10.1007/978-3-030-35802-0_18 ec_funded: 1 external_id: arxiv: - '1908.08129' isi: - '000612918800018' intvolume: ' 11904' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1908.08129 month: '11' oa: 1 oa_version: Preprint page: 230-243 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 27th International Symposium on Graph Drawing and Network Visualization publication_identifier: eissn: - 1611-3349 isbn: - 978-3-0303-5801-3 issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Extending simple drawings type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 11904 year: '2019' ... --- _id: '7401' abstract: - lang: eng text: 'The genus g(G) of a graph G is the minimum g such that G has an embedding on the orientable surface M_g of genus g. 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 Z_2-genus of a graph G, denoted by g_0(G), is the minimum g such that G has an independently even drawing on M_g. By a result of Battle, Harary, Kodama and Youngs from 1962, the graph genus is additive over 2-connected blocks. In 2013, Schaefer and Stefankovic proved that the Z_2-genus of a graph is additive over 2-connected blocks as well, and asked whether this result can be extended to so-called 2-amalgamations, as an analogue of results by Decker, Glover, Huneke, and Stahl for the genus. We give the following partial answer. If G=G_1 cup G_2, G_1 and G_2 intersect in two vertices u and v, and G-u-v has k connected components (among which we count the edge uv if present), then |g_0(G)-(g_0(G_1)+g_0(G_2))|<=k+1. For complete bipartite graphs K_{m,n}, with n >= m >= 3, we prove that g_0(K_{m,n})/g(K_{m,n})=1-O(1/n). Similar results are proved also for the Euler Z_2-genus. We express the Z_2-genus of a graph using the minimum rank of partial symmetric matrices over Z_2; a problem that might be of independent interest. ' alternative_title: - LIPIcs article_number: '39' article_processing_charge: No arxiv: 1 author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Jan full_name: Kyncl, Jan last_name: Kyncl citation: ama: 'Fulek R, Kyncl J. Z_2-Genus of graphs and minimum rank of partial symmetric matrices. In: 35th International Symposium on Computational Geometry (SoCG 2019). Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019. doi:10.4230/LIPICS.SOCG.2019.39' apa: 'Fulek, R., & Kyncl, J. (2019). Z_2-Genus of graphs and minimum rank of partial symmetric matrices. In 35th International Symposium on Computational Geometry (SoCG 2019) (Vol. 129). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.39' chicago: Fulek, Radoslav, and Jan Kyncl. “Z_2-Genus of Graphs and Minimum Rank of Partial Symmetric Matrices.” In 35th International Symposium on Computational Geometry (SoCG 2019), Vol. 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.39. ieee: R. Fulek and J. Kyncl, “Z_2-Genus of graphs and minimum rank of partial symmetric matrices,” in 35th International Symposium on Computational Geometry (SoCG 2019), Portland, OR, United States, 2019, vol. 129. ista: 'Fulek R, Kyncl J. 2019. Z_2-Genus of graphs and minimum rank of partial symmetric matrices. 35th International Symposium on Computational Geometry (SoCG 2019). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 129, 39.' mla: Fulek, Radoslav, and Jan Kyncl. “Z_2-Genus of Graphs and Minimum Rank of Partial Symmetric Matrices.” 35th International Symposium on Computational Geometry (SoCG 2019), vol. 129, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, doi:10.4230/LIPICS.SOCG.2019.39. short: R. Fulek, J. Kyncl, in:, 35th International Symposium on Computational Geometry (SoCG 2019), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. conference: end_date: 2019-06-21 location: Portland, OR, United States name: 'SoCG: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2020-01-29T16:17:05Z date_published: 2019-06-01T00:00:00Z date_updated: 2021-01-12T08:13:24Z day: '01' ddc: - '000' department: - _id: UlWa doi: 10.4230/LIPICS.SOCG.2019.39 external_id: arxiv: - '1903.08637' file: - access_level: open_access checksum: aac37b09118cc0ab58cf77129e691f8c content_type: application/pdf creator: dernst date_created: 2020-02-04T09:14:31Z date_updated: 2020-07-14T12:47:57Z file_id: '7445' file_name: 2019_LIPIcs_Fulek.pdf file_size: 628347 relation: main_file file_date_updated: 2020-07-14T12:47:57Z has_accepted_license: '1' intvolume: ' 129' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: 35th International Symposium on Computational Geometry (SoCG 2019) publication_identifier: isbn: - 978-3-95977-104-7 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Z_2-Genus of graphs and minimum rank of partial symmetric matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 129 year: '2019' ... --- _id: '7950' abstract: - lang: eng text: "The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices \ have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved." article_number: '1903.06981' article_processing_charge: No arxiv: 1 author: - first_name: Ahmad full_name: Biniaz, Ahmad last_name: Biniaz - first_name: Kshitij full_name: Jain, Kshitij last_name: Jain - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tillmann full_name: Miltzow, Tillmann last_name: Miltzow - first_name: Debajyoti full_name: Mondal, Debajyoti last_name: Mondal - first_name: Anurag Murty full_name: Naredla, Anurag Murty last_name: Naredla - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Alexi full_name: Turcotte, Alexi last_name: Turcotte citation: ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv. apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv. chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d. ieee: A. Biniaz et al., “Token swapping on trees,” arXiv. . ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981. mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981. short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.). date_created: 2020-06-08T12:25:25Z date_published: 2019-03-16T00:00:00Z date_updated: 2024-01-04T12:42:08Z day: '16' department: - _id: HeEd - _id: UlWa - _id: KrCh external_id: arxiv: - '1903.06981' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.06981 month: '03' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted related_material: record: - id: '7944' relation: dissertation_contains status: public - id: '12833' relation: later_version status: public status: public title: Token swapping on trees type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '8182' abstract: - lang: eng text: "Suppose that $n\\neq p^k$ and $n\\neq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $\\mathfrak S_n$ there exists an $\\mathfrak S_n$-equivariant map $X \\to\r\n{\\mathbb R}^n$ whose image avoids the diagonal $\\{(x,x\\dots,x)\\in {\\mathbb R}^n|x\\in {\\mathbb R}\\}$.\r\n Previously, the special cases of this statement for certain $X$ were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We\r\ntake a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of $\\mathfrak S_n$-equivariant maps from the boundary\r\n$\\partial\\Delta^{n-1}$ of $(n-1)$-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser's conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem." article_number: '1910.12628' article_processing_charge: No arxiv: 1 author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Sergey full_name: Kudrya, Sergey id: ecf01965-d252-11ea-95a5-8ada5f6c6a67 last_name: Kudrya citation: ama: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv. apa: Avvakumov, S., & Kudrya, S. (n.d.). Vanishing of all equivariant obstructions and the mapping degree. arXiv. arXiv. chicago: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv. arXiv, n.d. ieee: S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” arXiv. arXiv. ista: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv, 1910.12628. mla: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv, 1910.12628, arXiv. short: S. Avvakumov, S. Kudrya, ArXiv (n.d.). date_created: 2020-07-30T10:45:08Z date_published: 2019-10-28T00:00:00Z date_updated: 2023-09-07T13:12:17Z day: '28' department: - _id: UlWa external_id: arxiv: - '1910.12628' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.12628 month: '10' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted publisher: arXiv related_material: record: - id: '11446' relation: later_version status: public - id: '8156' relation: dissertation_contains status: public status: public title: Vanishing of all equivariant obstructions and the mapping degree type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '8184' abstract: - lang: eng text: "Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. " acknowledgement: We would like to thank F. Frick for helpful discussions article_number: '1908.08731' article_processing_charge: No arxiv: 1 author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: R. full_name: Karasev, R. last_name: Karasev - first_name: A. full_name: Skopenkov, A. last_name: Skopenkov citation: ama: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv. apa: Avvakumov, S., Karasev, R., & Skopenkov, A. (n.d.). Stronger counterexamples to the topological Tverberg conjecture. arXiv. arXiv. chicago: Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv. arXiv, n.d. ieee: S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the topological Tverberg conjecture,” arXiv. arXiv. ista: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv, 1908.08731. mla: Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv, 1908.08731, arXiv. short: S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.). date_created: 2020-07-30T10:45:34Z date_published: 2019-08-23T00:00:00Z date_updated: 2023-09-08T11:20:02Z day: '23' department: - _id: UlWa external_id: arxiv: - '1908.08731' isi: - '000986519600004' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1908.08731 month: '08' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted publisher: arXiv related_material: record: - id: '8156' relation: dissertation_contains status: public status: public title: Stronger counterexamples to the topological Tverberg conjecture type: preprint user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '8185' abstract: - lang: eng text: "In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi, Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment\r\npartition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power." article_number: '1907.11183' article_processing_charge: No arxiv: 1 author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv. doi:10.48550/arXiv.1907.11183 apa: Avvakumov, S., & Karasev, R. (n.d.). Envy-free division using mapping degree. arXiv. https://doi.org/10.48550/arXiv.1907.11183 chicago: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1907.11183. ieee: S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv. . ista: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv, 1907.11183. mla: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183. short: S. Avvakumov, R. Karasev, ArXiv (n.d.). date_created: 2020-07-30T10:45:51Z date_published: 2019-07-25T00:00:00Z date_updated: 2023-09-07T13:12:17Z day: '25' department: - _id: UlWa doi: 10.48550/arXiv.1907.11183 external_id: arxiv: - '1907.11183' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1907.11183 month: '07' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted related_material: link: - relation: later_version url: https://doi.org/10.1112/mtk.12059 record: - id: '8156' relation: dissertation_contains status: public status: public title: Envy-free division using mapping degree type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ...