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Claim. The conjecture of Problem 61 for $H$ the E-graph and for $H$ the Bird graph, both as the preprint's figures define them: Theorems 1.10 and 1.11 of S. Huang, Y. Ju and Y. Zhou, Erdős–Hajnal conjecture beyond five-vertex graphs, arXiv:2606.06258, posted 2026-06-04 (the claim's date) and revised 2026-06-08 and 2026-08-31. The E-graph is the five-vertex path with a pendant edge at its middle vertex; the Bird graph contains both $P_5$ and the bull as induced subgraphs. The preprint extends the iterative sparsification framework of Nguyen, Scott and Seymour with a generalized niceness condition, a property of combs and a structural lemma sufficient for the conjecture, and says that the framework recovers the $P_5$ and bull cases as special cases. Its abstract calls the two graphs the first six-vertex graphs whose case does not follow from the operations preserving the property, substitution and the degree-one extensions of Nguyen, Scott and Seymour's fourth paper.

Covers. Those two six-vertex graphs only, and the instances their complements share with them; the problem stays open.

Depends on. Nothing in this wiki. The comment on the third version (2026-08-31) says the proof no longer uses the five-vertex-path result.

Standing. Claimed: an unrefereed arXiv preprint, linked from the site's thread in a post of 5 June 2026, with no outside review known to this corpus; this corpus has not checked the proof.