Problem 108

Erdős Problem #108: declared status 'open'. Formalized: yes. For every $r\geq 4$ and $k\geq 2$ is there some finite $f(k,r)$ such that every graph of chromatic number $\geq f(k,r)$ contains a subgraph of girth $\geq r$ and chromatic number $\geq k$? Prize: no. Tags: chromatic number, cycles, graph theory.