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Polynomial bounds for chromatic number. III. Excluding a double star

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poly3.pdf (375.67 KB)

Date

2022-10

Authors

Scott, Alex
Seymour, Paul
Spirkl, Sophie

Journal Title

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Volume Title

Publisher

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.

Keywords

polynomial bounds, chromatic number, double star

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Citation

URI

https://doi.org/10.1002/jgt.22862
 http://hdl.handle.net/10012/18534

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Waterloo Research
Combinatorics and Optimization