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Claim. The paper proves the Erdős--Sós conjecture on trees in graphs, that a graph with average degree greater than $t-2$ contains every tree on $t\ge2$ vertices, which with $t=k+1$ is a strict-threshold form of the statement of Problem 548 and implies it. Its abstract describes the proof as a simplified one based on the recent resolution by GPT-6 Astra, written in the language of random cyclic orderings, and says that the paper also gives another proof of the corresponding conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé for antidirected trees in digraphs.

Claimant and postings. Bryce Frederickson, Erdős-Sós via random cyclic orderings, arXiv:2609.21159, v1 18 September 2026, the date this page is named by. A comment of 21 September 2026 in the site's discussion lists it. The argument rests on the proof recorded on Adamczewski 2026, whose Reviewed account cites this paper.

Standing. Claimed, not accepted: a preprint, not refereed, reviewed or formalized.

Depends on. Nothing in this wiki.

Read depth. The arXiv abstract and version record were read; the body was not.