Homogeneous sets, clique-separators, critical graphs, and optimal $\chi$-binding functions

Christoph Brause, Maximilian Geißer, Ingo Schiermeyer

Given a set $\mathcal{H}$ of graphs, let $f_{\mathcal{H}}^{\star }:{\mathbb{N}}_{>0}\to {\mathbb{N}}_{>0}$ be the optimal $\chi$-binding function of the class of $\mathcal{H}$-free graph…