Polynomial bounds for chromatic number. III. Excluding a double star
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Scott, Alex
Seymour, Paul
Spirkl, Sophie
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Wiley
Abstract
A “double star” is a tree with two internal vertices. It is known that the Gyárfás-Sumner conjecture
holds for double stars, that is, for every double star H, there is a function fH such that if G does
not contain H as an induced subgraph then x(G) ≤ fH(w(G)) (where x, w are the chromatic number
and the clique number of G). Here we prove that fH can be chosen to be a polynomial.
Description
This is the peer reviewed version of the following article: Scott, A., Seymour, P., & Spirkl, S. (2022). Polynomial bounds for chromatic number. III. Excluding a double star. Journal of Graph Theory, 101(2), 323–340. https://doi.org/10.1002/jgt.22862, which has been published in final form at https://doi.org/10.1002/jgt.22862. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.