Problem 640

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Statement. Let $k\geq 3$. Does there exist some $f(k)$ such that if a graph $G$ has chromatic number $\geq f(k)$ then $G$ must contain some odd cycle whose vertices span a graph of chromatic number $\geq k$?

Status. Open.

Source. erdosproblems.com/640, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #640, https://www.erdosproblems.com/640.

Formalization. None recorded.

Progress

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