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Claim. Theorem 1.1 (p. 2) of the preprint on the library's [[../library/ramsey_theory/montgomery_2025_ramsey_numbers_trees/_index|source card]], [[../library/ramsey_theory/montgomery_2025_ramsey_numbers_trees/theorem_1_1|Theorem 1.1]]: there is a constant $c>0$ such that every $n$-vertex tree $T$ with $\Delta(T)\le cn$ and bipartition classes of sizes $t_1\ge t_2$ satisfies

$$R(T)=\max\{2t_1,\,t_1+2t_2\}-1,$$

Burr's formula. With $t_1+t_2=n$ and $t_2\ge1$ for $n\ge2$, both $2t_1-1$ and $t_1+2t_2-1=n+t_2-1$ are at most $2n-2$, so every such tree satisfies the bound of the problem.

Covers. The corrected Statement of Problem 547 for every tree on $n\ge2$ vertices whose maximum degree is at most $cn$, with $c$ the preprint's unstated small constant. Every other tree is outside this claim; the full corrected Statement is settled by the accepted claim page [[problems/ramsey_theory/E0547/claims/2026_09_03_adamczewski|the 2026 claim]].

Depends on. Nothing in this wiki; the result is the preprint's own theorem.

Standing. Claimed, not accepted. R. Montgomery, M. Pavez-Signé and J. Yan, Ramsey numbers of trees, arXiv:2509.07934v1 (9 September 2025, the date this page is named by), 59 pages, under the CC BY 4.0 license; no journal version is known. The site's commentary records the result as [MPY25], but its label DECIDABLE settles neither the problem nor any part of it, so the credit is not acceptance evidence; nothing is refereed or formalized.