--- res: bibo_abstract: - '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.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Kristóf foaf_name: Huszár, Kristóf foaf_surname: Huszár foaf_workInfoHomepage: http://www.librecat.org/personId=33C26278-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-5445-5057 - foaf_Person: foaf_givenName: Jonathan foaf_name: Spreer, Jonathan foaf_surname: Spreer bibo_doi: 10.4230/LIPIcs.SoCG.2019.44 bibo_volume: 129 dct_date: 2019^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/1868-8969 - http://id.crossref.org/issn/978-3-95977-104-7 dct_language: eng dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@ dct_subject: - computational 3-manifold topology - fixed-parameter tractability - layered triangulations - structural graph theory - treewidth - cutwidth - Heegaard genus dct_title: 3-manifold triangulations with small treewidth@ ...