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.