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Problem #640: Is there some function $f$ such that for all $k\geq 3$ if a...

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...

Problem Statement

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 $\geq k$?
Categories: Graph Theory Chromatic Number

Progress

A problem of Erdős and Hajnal.

Source: erdosproblems.com/640 | Last verified: January 15, 2026

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