2 problems

Fix a graph $F$, and let ${\mathcal C}$ be a hereditary graph class. Say that ${\mathcal C}$ is chi-unbounded if its chromatic numbers are not bounded as a function of clique numbe…

Let $H$ be a graph, and let $\mathcal{F}(H)$ be the class of graphs excluding induced subdivisions of $H$. For a graph $G$, write $\omega(G)$ for its clique number, and let $k$ be…