Problem Statement
Does every graph $G$ with chromatic number $\geq \aleph_1$ contain all sufficiently large odd cycles?
Categories:
Graph Theory Set Theory
Progress
A problem of Erdős and Hajnal (who proved this for chromatic number $\geq \aleph_2$). This was proved by Erdős, Hajnal, and Shelah [EHS74].See also [593] and [737].
Source: erdosproblems.com/594 | Last verified: January 15, 2026