PROVED
This has been solved in the affirmative.
Let $G$ be a graph with chromatic number $\aleph_1$. Must there exist an edge $e$ such that, for all large $n$, $G$ contains a cycle of length $n$ containing $e$?
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Likes this problem
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Interested in collaborating
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Currently working on this problem
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This problem looks difficult
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This problem looks tractable
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The results on this problem could be formalisable
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I am working on formalising the results on this problem
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Additional thanks to: Boris Alexeev
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #737, https://www.erdosproblems.com/737, accessed 2026-04-11
