This paper deals with the minimum number mH(r) of edges in an H-free graph with the chromatic number more than r. We show how bounds on Ramsey and Tur\'an numbers imply bounds on mH(r).
@article{arxiv.2207.05840,
title = {Erd\H os--Hajnal problem for $H$-free hypergraphs},
author = {Danila Cherkashin and Alexei Gordeev and Georgii Strukov},
journal= {arXiv preprint arXiv:2207.05840},
year = {2022}
}