Polynomial chi-binding function for tbroom- free graphs

A graph class is called polynomially chibounded if there is a fixed function such that for every graph G in the graph class, the chromatic number of G is bounded by that function of the clique number of G. For any positive integer t, a t-broom is a graph obtained from a star on t+1 leaves by subdividing an edge once. A fork is graph obtained from a star on 4 leaves by subdividing two edges. In this talk, we show that the class of induced-t-broomfree graphs is polynomially chi-bounded, answering a question of Schiermeyer and Randerath. Joint work with Xiaonan Liu, Joshua Schroeder and Xingxing Yu.