Claims

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1966_03_01_erdos_hajnal: Erdős and Hajnal's theorem that a graph of uncountable chromatic number contains K_{i,aleph_1} for every finite i gives it a cycle of every length 2^m with m at least 2; the site credits David Penman with the observation.

2020_10_29_liu_montgomery: Liu and Montgomery's even-cycle interval theorem, with compactness, gives every graph of infinite chromatic number cycles of length a power of two for infinitely many exponents; the deduction is credited to Zach Hunter.

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