Polynomial bounds for chromatic number II: Excluding a star-forest
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Date
2022-10
Authors
Scott, Alex
Seymour, Paul
Spirkl, Sophie
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Abstract
The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G
is H-free then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of
G). Louis Esperet conjectured that, whenever such a statement holds, fH can be chosen to be a
polynomial. The Gyárfás–Sumner conjecture is only known to be true for a modest set of forests H,
and Esperet's conjecture is known to be true for almost no forests. For instance, it is not known
when H is a five-vertex path. Here we prove Esperet's conjecture when each component of H is a
star.
Description
This is the peer reviewed version of the following article: Scott, A., Seymour, P., & Spirkl, S. (2022). Polynomial bounds for chromatic number II: Excluding a star-forest. Journal of Graph Theory, 101(2), 318–322. https://doi.org/10.1002/jgt.22829, which has been published in final form at https://doi.org/10.1002/jgt.22829. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Keywords
chromatic number, induced subgraph, chi-boundedness, colouring, gyarfas-sumner conjecture