Problem 740

Erdős Problem #740: declared status 'open'. Formalized: yes. Let $\mathfrak{m}$ be an infinite cardinal and $G$ be a graph with chromatic number $\mathfrak{m}$. Let $r\geq 1$. Must $G$ contain a subgraph of chromatic number $\mathfrak{m}$ which does not contain any odd cycle of length $\leq r$? Prize: no. Tags: chromatic number, graph theory.