Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path
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Date
2023-09-15
Authors
Scott, Alex
Seymour, Paul
Spirkl, Sophie
Journal Title
Journal ISSN
Volume Title
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.
Description
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