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Claim. Every graph of diameter $2$ with minimum degree at least $3$ contains a cycle of length $4$ or $8$, so the conjecture of Problem 64 holds for graphs of diameter $2$. The result is Avery Carr, Cycles of length 4 or 8 in graphs with diameter 2 and minimum degree at least 3, arXiv:2508.19302, posted 2025-08-25 (the claim's date; v4 of 2026-01-30, twelve pages), whose arXiv comment reports acceptance for publication in the Bulletin of the Institute of Combinatorics and its Applications. Read depth: the arXiv record and abstract; the proof was not read. The thread comment of 6 December 2025 that the site's remark points to lists the paper among the families where the conjecture is confirmed, and Temeller's claim (claim page) extends the theorem to diameter $3$ at minimum degree $4$.

Covers. The statement of Problem 64 for graphs of diameter $2$, where the cycle found has length $2^2$ or $2^3$.

Depends on. No page of this wiki.

Standing. Claimed: the acceptance is author-reported on the arXiv record, and no published version with volume and pages is known to this corpus, so no refereed evidence is listed. 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 acceptance.