PROVED
This has been solved in the affirmative.
If $G$ is a graph with $4k$ vertices and minimum degree at least $2k$ then $G$ contains $k$ vertex-disjoint $4$-cycles.
A conjecture of Erdős and Faudree. Proved by Wang
[Wa10].
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T. F. Bloom, Erdős Problem #577, https://www.erdosproblems.com/577, accessed 2026-01-14