Problem 640

Erdős Problem #640: declared status 'open'. Formalized: no. Is there some function $f$ such that for all $k\geq 3$ if a finite graph $G$ has chromatic number $\geq f(k)$ then $G$ must contain some odd cycle whose vertices span a graph of chromatic number $\geq k$? Prize: no. Tags: chromatic number, graph theory.