---

Claim. Every graph with minimum degree at least $3$ and no induced path on ten vertices contains a cycle of length $4$ or $8$, so the conjecture of Problem 64 holds for $P_{10}$-free graphs, which include the $P_8$-free graphs of Gao and Shan (claim page). The result is Zhiquan Hu and Changlong Shen, The Erdős-Gyárfás conjecture holds for $P_{10}$-free graphs, Discrete Math. 347 (2024), no. 12, Paper No. 114175, doi:10.1016/j.disc.2024.114175, whose Crossref record dates the issue to December 2024 without a day, first posted as Erdős--Gyárfás conjecture for $P_{10}$-free graphs, arXiv:2308.05675, on 2023-08-10 (the claim's date; v2 of 2023-08-12). Read depth (2026-10-07): 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 $P_{10}$-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 Discrete Mathematics. 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.