Polynomial bounds for chromatic number II: Excluding a star-forest
| dc.contributor.author | Scott, Alex | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-08-12T01:18:17Z | |
| dc.date.available | 2022-08-12T01:18:17Z | |
| dc.date.issued | 2022-10 | |
| dc.description | This is the peer reviewed version of the following article: Scott, A., Seymour, P., & Spirkl, S. (2022). Polynomial bounds for chromatic number II: Excluding a star-forest. Journal of Graph Theory, 101(2), 318–322. https://doi.org/10.1002/jgt.22829, which has been published in final form at https://doi.org/10.1002/jgt.22829. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. | en |
| dc.description.abstract | The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G is H-free then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of G). Louis Esperet conjectured that, whenever such a statement holds, fH can be chosen to be a polynomial. The Gyárfás–Sumner conjecture is only known to be true for a modest set of forests H, and Esperet's conjecture is known to be true for almost no forests. For instance, it is not known when H is a five-vertex path. Here we prove Esperet's conjecture when each component of H is a star. | en |
| dc.description.sponsorship | Research supported by EPSRC grant EP/V007327/1. Supported by AFOSR grant A9550-19-1-0187, and by NSF grant DMS-1800053. We 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/10.1002/jgt.22829 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18535 | |
| dc.language.iso | en | en |
| dc.publisher | Wiley | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | chromatic number | en |
| dc.subject | induced subgraph | en |
| dc.subject | chi-boundedness | en |
| dc.subject | colouring | en |
| dc.subject | gyarfas-sumner conjecture | en |
| dc.title | Polynomial bounds for chromatic number II: Excluding a star-forest | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Scott, A., Seymour, P., & Spirkl, S. (2022). Polynomial bounds for chromatic number II: Excluding a star-forest. Journal of Graph Theory, 101(2), 318–322. https://doi.org/10.1002/jgt.22829 | 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 |