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Claim. Every Cayley graph of minimum degree at least $3$ whose order is $2p^2$ or $4p$, for a prime $p$, contains a cycle whose length is a power of $2$. The result is Mohsen Ghasemi and Rezvan Varmazyar, On the Erdős--Gyárfás conjecture for some Cayley graphs, Mat. Vesnik 73 (2021), no. 1, 37--42. The page name carries the publication year; the day is not recorded in any source read. Read depth: the zbMATH record (Zbl 1474.05221) and its summary; the paper's text was not read. The thread comment of 6 December 2025 that the site's remark on Problem 64 points to lists the paper among the families where the conjecture is confirmed.

Covers. The statement of Problem 64 for Cayley graphs of order $2p^2$ and of order $4p$.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper is a publication in Matematički Vesnik, the journal of the Mathematical Society of Serbia. The site's curator cites the family list that names the paper while labeling the problem FALSIFIABLE, which is commentary on an open problem and not reviewed evidence.