Claims

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1967_01_01_gerencser_gyarfas: Theorem 1 of Gerencsér and Gyárfás (Ann. Univ. Sci. Budapest. 1967) gives the path on n vertices the Ramsey number n - 1 + floor(n/2), at most 2n - 2: the corrected statement of Problem 547 for every path.

1979_01_01_grossman_harary_klawe: Theorem 3.1 of Grossman, Harary and Klawe (Discrete Math. 1979) bounds the Ramsey number of every double star S(n,m) by 2n + m + 2, at most 2N - 2 on its N vertices: the corrected statement of Problem 547 for double stars.

2011_02_04_zhao: Corollary 2.2 of Zhao's proof of Loebl's conjecture for large n (Electron. J. Combin. 2011): every tree on n vertices has Ramsey number at most 2n minus 2 once n is large; the threshold is not explicit.

2025_09_09_montgomery_pavez_signe_yan: A 2025 preprint proving R(T) = max(2t_1, t_1 + 2t_2) - 1 for every tree T with maximum degree at most cn, at most 2n - 2: the corrected statement of Problem 547 for those trees; a preprint credited in the site's remarks.

2026_08_26_alexeev: A Lean development in Alexeev's repository proves, by its own route, that every tree on n vertices has Ramsey number at most 2n minus 2 once n is large; the threshold is not explicit, and it is not built here.

2026_08_26_alexeev_literal: Answers the site's wording (every n, the one-vertex tree included), not the corrected Statement (trees on n at least 2 vertices), so it does not count toward the problem's standing. Two Lean theorems in Alexeev's repository prove the site's wording false for the one-vertex tree.

2026_09_03_adamczewski: The sharp tree-free edge bound proved for Problem 548 (a GPT-6 Astra proof in Adamczewski's repository) gives R(T) at most 2n minus 2 for every tree on n at least 2 vertices; accepted on a third party's Lean proof built here.

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