Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Claim. Every -connected cubic planar graph contains a cycle whose length is a power of . The result is Christopher Carl Heckman and Roi Krakovski, Erdős--Gyárfás conjecture for cubic planar graphs, Electron. J. Combin. 20 (2013), no. 2, Paper P7, 43 pp., published 2013-04-09 (the claim's date). The abstract describes the proof as long, computer-based in parts, and a novel use of the discharging method. Read depth: the journal record and abstract; the proof 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 -connected cubic planar graphs.
Depends on. No page of this wiki.
Acceptance. Refereed: the paper is a publication in the Electronic Journal of Combinatorics. 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.