Polynomial bounds for chromatic number VII. Disjoint holes.
dc.contributor.author | Chudnovsky, Maria | |
dc.contributor.author | Scott, Alex | |
dc.contributor.author | Seymour, Paul | |
dc.contributor.author | Spirkl, Sophie | |
dc.date.accessioned | 2023-09-19T18:28:07Z | |
dc.date.available | 2023-09-19T18:28:07Z | |
dc.date.issued | 2023-11 | |
dc.description.abstract | A hole in a graph G is an induced cycle of length at least four, and a k-multihole in G is the union of k pairwise disjoint and nonneighbouring holes. It is well know that if G does not contain any holes then its chromatic number is equal to its clique number. In this paper we show that, for any integer k >- 1, if G does not contain a k-multihole, then its chromatic number is at most a polynomial function of its clique number. We show that the same result holds if we ask for all the holes to be odd or of length four; and if we ask for the holes to be longer than any fixed constant or of length four. This is part of a broader study of graph classes that are polynomially x-bounded. | en |
dc.description.sponsorship | Engineering and Physical Sciences Research Council, EP/V007327/1 || Air Force Office of Scientific Research, A9550-019-1-0187, FA9550-22-1-0234 || Natural Sciences and Engineering Research Council of Canada, RGPIN-2020-03912 || National Science Foundation, DMS-2120644, DMS-2154169. | en |
dc.identifier.uri | https://doi.org/10.1002/jgt.22987 | |
dc.identifier.uri | http://hdl.handle.net/10012/19888 | |
dc.language.iso | en | en |
dc.publisher | Wiley | en |
dc.relation.ispartofseries | Journal of Graph Theory;104(3) | |
dc.rights | Attribution 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | colouring | en |
dc.subject | induced subgraph | en |
dc.subject | x-boundedness | en |
dc.title | Polynomial bounds for chromatic number VII. Disjoint holes. | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Chudnovsky, M., Scott, A., Seymour, P., & Spirkl, S. (2023). Polynomial bounds for chromatic number VII. disjoint holes. Journal of Graph Theory 104(3). https://doi.org/10.1002/jgt.22987 | 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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