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Claim. Every graph with minimum degree at least $3$ and no induced path on eight vertices contains a cycle of length $4$ or $8$, so the conjecture of Problem 64 holds for $P_8$-free graphs. The result is Yuping Gao and Songling Shan, Erdős--Gyárfás conjecture for $P_8$-free graphs, Graphs Combin. 38 (2022), no. 6, Paper No. 168, doi:10.1007/s00373-022-02578-9, published 2022-10-10, first posted as arXiv:2109.01277 on 2021-09-03 (the claim's date), ten pages. Read depth: the arXiv record and abstract and the journal's Crossref record; 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.

Covers. The statement of Problem 64 for $P_8$-free graphs, where the cycle found has length $2^2$ or $2^3$.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper is a publication in Graphs and 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.