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Polynomial bounds for chromatic number VII. Disjoint holes.

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Journal of Graph Theory - 2023 - Chudnovsky.pdf (704.35 KB)

Date

2023-11

Authors

Chudnovsky, Maria
Scott, Alex
Seymour, Paul
Spirkl, Sophie

Journal Title

Journal ISSN

Volume Title

Publisher

Wiley

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.

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Keywords

colouring, induced subgraph, x-boundedness

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Citation

URI

https://doi.org/10.1002/jgt.22987
 http://hdl.handle.net/10012/19888

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Waterloo Research