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Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path

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s00493-023-00015-w.pdf (223.42 KB)

Date

2023-09-15

Authors

Scott, Alex
Seymour, Paul
Spirkl, Sophie

Journal Title

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Publisher

Springer

Abstract

A graph G is H -free if it has no induced subgraph isomorphic to H. We prove that a P5-free graph with clique number ω ≥ 3 has chromatic number at most ωlog2(ω). The best previous result was an exponential upper bound (5/27)3ω, due to Esperet, Lemoine, Maffray, and Morel. A polynomial bound would imply that the celebrated Erd˝os-Hajnal conjecture holds for P5, which is the smallest open case. Thus, there is great interest in whether there is a polynomial bound for P5-free graphs, and our result is an attempt to approach that.

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This article is made available open access through a Creative Commons Attribution 4.0 International license http://creativecommons.org/licenses/by/4.0/

Keywords

chromatic number, induced subgraphs

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URI

https://doi.org/10.1007/s00493-023-00015-w
 http://hdl.handle.net/10012/20133

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Waterloo Research