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Claim. Every $K_{1,m}$-free graph with minimum degree at least $m+1$, and every $K_{1,m}$-free graph with minimum degree at least $3$ and maximum degree at least $2m-1$, contains a cycle whose length is a power of $2$. The result is Stephen E. Shauger, Results on the Erdős--Gyárfás conjecture in $K_{1,m}$-free graphs, Congr. Numer. 134 (1998), 61--65; the paper also gives lower bounds on the number of vertices of a claw-free cubic counterexample and of a claw-free counterexample of minimum degree $3$. The page name carries the publication year; the day is not recorded in any source read. The paper is not held by this corpus; the statement follows the zbMATH record (Zbl 0952.05038) and the thread comment of 6 December 2025 that the site's remark on Problem 64 points to for the families where the conjecture is confirmed.

Covers. The statement of Problem 64 for $K_{1,m}$-free graphs of minimum degree at least $m+1$, and for $K_{1,m}$-free graphs of maximum degree at least $2m-1$; for $m=3$ these are the claw-free graphs of minimum degree at least $4$ or maximum degree at least $5$.

Depends on. No page of this wiki.

Standing. Claimed: Congressus Numerantium is a proceedings series, and no evidence that the volume was refereed is recorded, so the publication is not listed as refereed evidence. 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.