In-Person Talk 

We prove that for every graph F with at least one edge there are graphs H of arbitrarily large chromatic number and the same clique number as F such that every F-free induced subgraph of H has chromatic number at most c=c(F). (Here a graph is F-free if it does not contain an induced copy of F.) This generalizes theorems of Brianski, Davies and Walczak, and of Carbonero, Hompe, Moore and Spirkl. We further show an analogous statement where clique number is replaced by odd girth.

Joint work with Antonio Girao, Freddie Illingworth, Emil Powierski, Michael Savery, Youri Tamitegama and Jane Tan.