Virtual Discrete Math Colloquium

The Gyárfás-Sumner conjecture says that for every forest $H$, there is a function $f$ such that the chromatic number $\chi (G)$ is at most $f(\omega (G))$ for every $H$-free graph $G$ ("$H$-free" means with no induced subgraph isomorphic to $H$, and $\omega (G)$ is the size of the largest clique of $G$). This well-known conjecture has been proved only for a …