James Davies

We prove that there is a function $f:\mathbb{N}\to \mathbb{N}$ such that for every function $g:\mathbb{N}\to \mathbb{N}\cup \{\mathrm{\infty }\}$ with $g(1)=1$ and $g\ge f$, there is a hereditary class of graphs $\mathcal{G}$ such that for each $\omega \in \mathbb{N}$, the maximum chromatic number of a graph in $\mathcal{G}$ with …