--- _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: '7962' abstract: - lang: eng text: 'A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: Bruce full_name: Reed, Bruce last_name: Reed - first_name: Yelena full_name: Yuditsky, Yelena last_name: Yuditsky citation: ama: Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917. doi:10.1007/s00454-020-00213-z apa: Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00213-z chicago: Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z. ieee: J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” Discrete and Computational Geometry, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020. ista: Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917. mla: Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z. short: J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917. date_created: 2020-06-14T22:00:51Z date_published: 2020-06-05T00:00:00Z date_updated: 2023-08-21T08:49:18Z day: '05' department: - _id: HeEd doi: 10.1007/s00454-020-00213-z external_id: arxiv: - '1803.06710' isi: - '000538229000001' intvolume: ' 63' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1803.06710 month: '06' oa: 1 oa_version: Preprint page: 888-917 project: - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize 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: Almost all string graphs are intersection graphs of plane convex sets type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2020' ... --- _id: '8323' article_processing_charge: No article_type: letter_note author: - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach citation: ama: Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5 apa: Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5 chicago: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5. ieee: J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020. ista: Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574. mla: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5. short: J. Pach, Discrete and Computational Geometry 64 (2020) 571–574. date_created: 2020-08-30T22:01:12Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-08-22T09:05:04Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-020-00237-5 external_id: isi: - '000561483500001' intvolume: ' 64' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00454-020-00237-5 month: '10' oa: 1 oa_version: None page: 571-574 publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer Nature scopus_import: '1' status: public title: A farewell to Ricky Pollack type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 64 year: '2020' ... --- _id: '7666' abstract: - lang: eng text: Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups. acknowledgement: This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Katharina full_name: Ölsböck, Katharina id: 4D4AA390-F248-11E8-B48F-1D18A9856A87 last_name: Ölsböck orcid: 0000-0002-4672-8297 citation: ama: Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x apa: Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00188-x chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00188-x. ieee: H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775, 2020. ista: Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775. mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x. short: H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775. date_created: 2020-04-19T22:00:56Z date_published: 2020-03-20T00:00:00Z date_updated: 2023-08-21T06:13:48Z day: '20' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00454-020-00188-x ec_funded: 1 external_id: isi: - '000520918800001' file: - access_level: open_access checksum: f8cc96e497f00c38340b5dafe0cb91d7 content_type: application/pdf creator: dernst date_created: 2020-11-20T13:22:21Z date_updated: 2020-11-20T13:22:21Z file_id: '8786' file_name: 2020_DiscreteCompGeo_Edelsbrunner.pdf file_size: 701673 relation: main_file success: 1 file_date_updated: 2020-11-20T13:22:21Z has_accepted_license: '1' intvolume: ' 64' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 759-775 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes 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: Tri-partitions and bases of an ordered complex 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 64 year: '2020' ... --- _id: '5678' abstract: - lang: eng text: "The order-k Voronoi tessellation of a locally finite set \U0001D44B⊆ℝ\U0001D45B decomposes ℝ\U0001D45B into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2 apa: Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2 chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2. ieee: H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019. ista: Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878. mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2. short: H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878. date_created: 2018-12-16T22:59:20Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-09-07T12:07:12Z day: '01' ddc: - '516' department: - _id: HeEd doi: 10.1007/s00454-018-0049-2 ec_funded: 1 external_id: arxiv: - '1709.09380' isi: - '000494042900008' file: - access_level: open_access checksum: f9d00e166efaccb5a76bbcbb4dcea3b4 content_type: application/pdf creator: dernst date_created: 2019-02-06T10:10:46Z date_updated: 2020-07-14T12:47:10Z file_id: '5932' file_name: 2018_DiscreteCompGeometry_Edelsbrunner.pdf file_size: 599339 relation: main_file file_date_updated: 2020-07-14T12:47:10Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 865–878 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '6287' relation: dissertation_contains status: public scopus_import: '1' status: public title: Poisson–Delaunay Mosaics of Order k 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 62 year: '2019' ... --- _id: '1064' abstract: - lang: eng text: 'In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets.' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy - first_name: Mikhail full_name: Grigorev, Mikhail last_name: Grigorev citation: ama: Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x apa: Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x chicago: Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x. ieee: A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018. ista: Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009. mla: Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x. short: A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009. date_created: 2018-12-11T11:49:57Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-20T12:08:51Z day: '01' ddc: - '516' - '000' department: - _id: HeEd doi: 10.1007/s00454-017-9883-x ec_funded: 1 external_id: isi: - '000432205500011' file: - access_level: open_access content_type: application/pdf creator: dernst date_created: 2019-01-18T09:27:36Z date_updated: 2019-01-18T09:27:36Z file_id: '5844' file_name: 2018_DiscreteComp_Akopyan.pdf file_size: 482518 relation: main_file success: 1 file_date_updated: 2019-01-18T09:27:36Z has_accepted_license: '1' intvolume: ' 59' isi: 1 issue: '4' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1001-1009 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Discrete & Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer publist_id: '6324' quality_controlled: '1' scopus_import: '1' status: public title: On the circle covering theorem by A.W. Goodman and R.E. Goodman 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: 59 year: '2018' ... --- _id: '1073' abstract: - lang: eng text: Let X and Y be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group G. Assuming that Y is d-connected and dimX≤2d, for some d≥1, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps |X|→|Y|; the existence of such a map can be decided even for dimX≤2d+1. This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into Rn under the condition k≤23n−1. More generally, we present an algorithm that, given a lifting-extension problem satisfying an appropriate stability assumption, computes the set of all homotopy classes of solutions. This result is new even in the non-equivariant situation. article_processing_charge: No author: - first_name: Martin full_name: Čadek, Martin last_name: Čadek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Lukáš full_name: Vokřínek, Lukáš last_name: Vokřínek citation: ama: Čadek M, Krcál M, Vokřínek L. Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. 2017;54(4):915-965. doi:10.1007/s00454-016-9855-6 apa: Čadek, M., Krcál, M., & Vokřínek, L. (2017). Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9855-6 chicago: Čadek, Martin, Marek Krcál, and Lukáš Vokřínek. “Algorithmic Solvability of the Lifting Extension Problem.” Discrete & Computational Geometry. Springer, 2017. https://doi.org/10.1007/s00454-016-9855-6. ieee: M. Čadek, M. Krcál, and L. Vokřínek, “Algorithmic solvability of the lifting extension problem,” Discrete & Computational Geometry, vol. 54, no. 4. Springer, pp. 915–965, 2017. ista: Čadek M, Krcál M, Vokřínek L. 2017. Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. 54(4), 915–965. mla: Čadek, Martin, et al. “Algorithmic Solvability of the Lifting Extension Problem.” Discrete & Computational Geometry, vol. 54, no. 4, Springer, 2017, pp. 915–65, doi:10.1007/s00454-016-9855-6. short: M. Čadek, M. Krcál, L. Vokřínek, Discrete & Computational Geometry 54 (2017) 915–965. date_created: 2018-12-11T11:50:00Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T12:01:28Z day: '01' department: - _id: UlWa doi: 10.1007/s00454-016-9855-6 external_id: isi: - '000400072700008' intvolume: ' 54' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1307.6444 month: '06' oa: 1 oa_version: Submitted Version page: 915 - 965 publication: Discrete & Computational Geometry publication_identifier: issn: - '01795376' publication_status: published publisher: Springer publist_id: '6309' quality_controlled: '1' scopus_import: '1' status: public title: Algorithmic solvability of the lifting extension problem type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 54 year: '2017' ... --- _id: '534' abstract: - lang: eng text: We investigate the complexity of finding an embedded non-orientable surface of Euler genus g in a triangulated 3-manifold. This problem occurs both as a natural question in low-dimensional topology, and as a first non-trivial instance of embeddability of complexes into 3-manifolds. We prove that the problem is NP-hard, thus adding to the relatively few hardness results that are currently known in 3-manifold topology. In addition, we show that the problem lies in NP when the Euler genus g is odd, and we give an explicit algorithm in this case. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Benjamin full_name: Burton, Benjamin last_name: Burton - first_name: Arnaud N full_name: De Mesmay, Arnaud N id: 3DB2F25C-F248-11E8-B48F-1D18A9856A87 last_name: De Mesmay - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Burton B, de Mesmay AN, Wagner U. Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. 2017;58(4):871-888. doi:10.1007/s00454-017-9900-0 apa: Burton, B., de Mesmay, A. N., & Wagner, U. (2017). Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9900-0 chicago: Burton, Benjamin, Arnaud N de Mesmay, and Uli Wagner. “Finding Non-Orientable Surfaces in 3-Manifolds.” Discrete & Computational Geometry. Springer, 2017. https://doi.org/10.1007/s00454-017-9900-0. ieee: B. Burton, A. N. de Mesmay, and U. Wagner, “Finding non-orientable surfaces in 3-Manifolds,” Discrete & Computational Geometry, vol. 58, no. 4. Springer, pp. 871–888, 2017. ista: Burton B, de Mesmay AN, Wagner U. 2017. Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. 58(4), 871–888. mla: Burton, Benjamin, et al. “Finding Non-Orientable Surfaces in 3-Manifolds.” Discrete & Computational Geometry, vol. 58, no. 4, Springer, 2017, pp. 871–88, doi:10.1007/s00454-017-9900-0. short: B. Burton, A.N. de Mesmay, U. Wagner, Discrete & Computational Geometry 58 (2017) 871–888. date_created: 2018-12-11T11:47:01Z date_published: 2017-06-09T00:00:00Z date_updated: 2023-02-21T17:01:34Z day: '09' department: - _id: UlWa doi: 10.1007/s00454-017-9900-0 external_id: arxiv: - '1602.07907' intvolume: ' 58' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1602.07907 month: '06' oa: 1 oa_version: Preprint page: 871 - 888 publication: Discrete & Computational Geometry publication_identifier: issn: - '01795376' publication_status: published publisher: Springer publist_id: '7283' quality_controlled: '1' related_material: record: - id: '1379' relation: earlier_version status: public scopus_import: 1 status: public title: Finding non-orientable surfaces in 3-Manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 year: '2017' ...