Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. Every cubic graph on fewer than vertices contains a cycle whose length is a power of , so a cubic counterexample to the conjecture of Problem 64 has at least vertices. The result is reported in Klas Markström, Extremal graphs for some problems on cycles in graphs, Congr. Numer. 171 (2004), 179--192, a collection of extremal graphs found by exhaustive computer search, among them the graphs without cycles of length and relating to the conjecture. 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 1063.05073), the thread comment of 6 December 2025 that the site's remark points to, and the account in the claw-free paper of Salehi Nowbandegani, Esfandiari, Shirdareh Haghighi and Bibak (claim page), which cites the bound as asserted by computer search.
Covers. The statement of Problem 64 for cubic graphs on at most vertices.
Depends on. No page of this wiki.
Standing. Claimed: Congressus Numerantium is a proceedings series with no recorded evidence of refereeing, and the search is author-reported, with no certificate or replay known to this corpus. 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.