Induced Subgraphs and Tree Decompositions III. Three-Path-Configurations and Logarithmic Treewidth.
| dc.contributor.author | Abrishami, Tara | |
| dc.contributor.author | Chudnovsky, Maria | |
| dc.contributor.author | Hajebi, Sepehr | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-09-20T14:39:23Z | |
| dc.date.available | 2022-09-20T14:39:23Z | |
| dc.date.issued | 2022-09-09 | |
| dc.description.abstract | A 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.sponsorship | Supported 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.identifier.uri | https://doi.org/10.19086/aic.2022.6 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18756 | |
| dc.language.iso | en | en |
| dc.publisher | Advances in Combinatorics | en |
| dc.relation.ispartofseries | Advances in Combinatorics; | |
| dc.rights | Attribution 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
| dc.title | Induced Subgraphs and Tree Decompositions III. Three-Path-Configurations and Logarithmic Treewidth. | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Carbonero, 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.2022.09.001 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |