Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree
| dc.contributor.author | Scott, Alex | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2023-02-21T19:51:39Z | |
| dc.date.available | 2023-02-21T19:51:39Z | |
| dc.date.issued | 2022-09-07 | |
| dc.description.abstract | Let H be a tree. It was proved by Rödl that graphs that do not contain H as an induced subgraph, and do not contain the complete bipartite graph Kt,t as a subgraph, have bounded chromatic number. Kierstead and Penrice strengthened this, showing that such graphs have bounded degeneracy. Here we give a further strengthening, proving that for every tree H, the degeneracy is at most polynomial in t. This answers a question of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak. | en |
| dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC), EP/V007327/1 || Air Force Office of Scientific Research (AFOSR), A9550-19-1-0187 || Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2020-03912 | en |
| dc.identifier.uri | https://doi.org/10.1002/jgt.22880 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19177 | |
| dc.language.iso | en | en |
| dc.publisher | Wiley | en |
| dc.relation.ispartofseries | Journal of Graph Theory; | |
| dc.rights | Attribution 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
| dc.subject | bipartite graphs | en |
| dc.subject | induced subgraphs | en |
| dc.title | Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Scott, A., Seymour, P., & Spirkl, S. (2022). Polynomial bounds for chromatic number. I. Excluding a Biclique and an induced tree. Journal of Graph Theory, 102(3), 458–471. https://doi.org/10.1002/jgt.22880 | 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 |
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