Scott, AlexSeymour, PaulSpirkl, Sophie2022-08-122022-08-122022-10https://doi.org/10.1002/jgt.22829http://hdl.handle.net/10012/18535This 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.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.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/chromatic numberinduced subgraphchi-boundednesscolouringgyarfas-sumner conjectureArticle