Open on erdosproblems.com (label OPEN, accessed 2026-10-07). The site's notes call it a question of Erdős and Hajnal, record Rödl's theorem for $\mathfrak{m}=\aleph_0$ and $r=3$, and say that Erdős and Hajnal asked more generally for an $f_r(\mathfrak{m})$ such that chromatic number at least $f_r(\mathfrak{m})$ forces a subgraph of chromatic number $\mathfrak{m}$ with no odd cycle of length at most $r$. The label does not record the refereed consistency result of Komjáth and Shelah (1988), under which the statement, as a question about every infinite cardinal, is not a theorem of ZFC; that result is one side of an independence result and leaves the problem open, as the label does. A refutation in ZFC alone, Johan Land's 2026 claim, is pending.