--- _id: '6556' abstract: - lang: eng text: 'Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field.' alternative_title: - LIPIcs 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 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer citation: ama: 'Huszár K, Spreer J. 3-manifold triangulations with small treewidth. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:44:1-44:20. doi:10.4230/LIPIcs.SoCG.2019.44' apa: 'Huszár, K., & Spreer, J. (2019). 3-manifold triangulations with small treewidth. In 35th International Symposium on Computational Geometry (Vol. 129, p. 44:1-44:20). Portland, Oregon, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2019.44' chicago: Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small Treewidth.” In 35th International Symposium on Computational Geometry, 129:44:1-44:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPIcs.SoCG.2019.44. ieee: K. Huszár and J. Spreer, “3-manifold triangulations with small treewidth,” in 35th International Symposium on Computational Geometry, Portland, Oregon, United States, 2019, vol. 129, p. 44:1-44:20. ista: 'Huszár K, Spreer J. 2019. 3-manifold triangulations with small treewidth. 35th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 129, 44:1-44:20.' mla: Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small Treewidth.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20, doi:10.4230/LIPIcs.SoCG.2019.44. short: K. Huszár, J. Spreer, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20. conference: end_date: 2019-06-21 location: Portland, Oregon, United States name: 'SoCG: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2019-06-11T20:09:57Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-07T13:18:26Z day: '01' ddc: - '516' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2019.44 external_id: arxiv: - '1812.05528' file: - access_level: open_access checksum: 29d18c435368468aa85823dabb157e43 content_type: application/pdf creator: kschuh date_created: 2019-06-12T06:45:33Z date_updated: 2020-07-14T12:47:33Z file_id: '6557' file_name: 2019_LIPIcs-Huszar.pdf file_size: 905885 relation: main_file file_date_updated: 2020-07-14T12:47:33Z has_accepted_license: '1' intvolume: ' 129' keyword: - computational 3-manifold topology - fixed-parameter tractability - layered triangulations - structural graph theory - treewidth - cutwidth - Heegaard genus language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version page: 44:1-44:20 publication: 35th International Symposium on Computational Geometry publication_identifier: isbn: - 978-3-95977-104-7 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '8032' relation: part_of_dissertation status: public scopus_import: '1' status: public title: 3-manifold triangulations with small treewidth 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' ...