A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number
| dc.contributor.author | Carbonero, Alvaro | |
| dc.contributor.author | Hompe, Patrick | |
| dc.contributor.author | Moore, Benjamin | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-09-20 14:39:45 (GMT) | |
| dc.date.available | 2022-09-20 14:39:45 (GMT) | |
| dc.date.issued | 2023-01 | |
| dc.identifier.uri | https://doi.org/10.1016/j.jctb.2022.09.001 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18757 | |
| dc.description | The 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.abstract | We 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.sponsorship | We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-03912]. | en |
| dc.language.iso | en | en |
| dc.publisher | Elsevier ScienceDirect | en |
| dc.relation.ispartofseries | Journal of Combinatorial Theory, Series B; | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | χ-Boundedness | en |
| dc.subject | induced subgraph | en |
| dc.subject | directed graph | en |
| dc.title | A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number | 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.typeOfResource | Text | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
Files in this item
This item appears in the following Collection(s)
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 International