A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number

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dc.contributor.authorCarbonero, Alvaro
dc.contributor.authorHompe, Patrick
dc.contributor.authorMoore, Benjamin
dc.contributor.authorSpirkl, Sophie
dc.date.accessioned2022-09-20T14:39:45Z
dc.date.available2022-09-20T14:39:45Z
dc.date.issued2023-01
dc.descriptionThe final publication is available at Elsevier via https://doi.org/10.1016/j.jctb.2022.09.001 © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.description.abstractWe prove that for every n, there is a graph G with χ(G) ≥ n and ω(G) ≤ 3 such that every induced subgraph H of G with ω(H) ≤ 2 satisfies χ(H) ≤ 4.This disproves a well-known conjecture. Our construction is a digraph with bounded clique number, large dichromatic number, and no induced directed cycles of odd length at least 5.en
dc.description.sponsorshipWe acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-03912].en
dc.identifier.urihttps://doi.org/10.1016/j.jctb.2022.09.001
dc.identifier.urihttp://hdl.handle.net/10012/18757
dc.language.isoenen
dc.publisherElsevier ScienceDirecten
dc.relation.ispartofseriesJournal of Combinatorial Theory, Series B;
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectχ-Boundednessen
dc.subjectinduced subgraphen
dc.subjectdirected graphen
dc.titleA Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Numberen
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.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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