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dc.contributor.authorAbrishami, Tara
dc.contributor.authorChudnovsky, Maria
dc.contributor.authorHajebi, Sepehr
dc.contributor.authorSpirkl, Sophie
dc.date.accessioned2022-09-20 14:39:23 (GMT)
dc.date.available2022-09-20 14:39:23 (GMT)
dc.date.issued2022-09-09
dc.identifier.urihttps://doi.org/10.19086/aic.2022.6
dc.identifier.urihttp://hdl.handle.net/10012/18756
dc.description.abstractA theta is a graph consisting of two non-adjacent vertices and three internally disjoint paths between them, each of length at least two. For a family H of graphs, we say a graph G is H-free if no induced subgraph of G is isomorphic to a member of H. We prove a conjecture of Sintiari and Trotignon, that there exists an absolute constant c for which every (theta, triangle)-free graph G has treewidth at most c log(jV(G)j). A construction by Sintiari and Trotignon shows that this bound is asymptotically best possible, and (theta, triangle)-free graphs comprise the first known hereditary class of graphs with arbitrarily large yet logarithmic treewidth. Our main result is in fact a generalization of the above conjecture, that treewidth is at most logarithmic in jV(G)j for every graph G excluding the so-called three-path-configurations as well as a fixed complete graph. It follows that several NP-hard problems such as STABLE SET, VERTEX COVER, DOMINATING SET and COLORING admit polynomial time algorithms in graphs excluding the three-path-configurations and a fixed complete graph.en
dc.description.sponsorshipSupported by NSF Grant DMS-1763817 and NSF-EPSRC Grant DMS-2120644. The authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-03912].en
dc.language.isoenen
dc.publisherAdvances in Combinatoricsen
dc.relation.ispartofseriesAdvances in Combinatorics;
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.titleInduced Subgraphs and Tree Decompositions III. Three-Path-Configurations and Logarithmic Treewidth.en
dc.typeArticleen
dcterms.bibliographicCitationCarbonero, A., Hompe, P., Moore, B., & Spirkl, S. (2023). A counterexample to a conjecture about triangle-free induced subgraphs of graphs with large chromatic number. Journal of Combinatorial Theory, Series B, 158, 63–69. https://doi.org/10.1016/j.jctb.2022.09.001en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen
uws.typeOfResourceTexten
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen


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