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Claim. Write $S(n,m)$, $n\ge m$, for the double star formed by joining the centers of $K_{1,n}$ and $K_{1,m}$ by an edge. Norin, Sun and Zhao prove (Theorem 1.3 of the library's source card) that for $n\ge2m$

$$r(S(n,m))\ge\tfrac{21}{23}m+\tfrac{189}{115}n+o(m).$$

At $n=2k-1$, $m=k-1$ the tree $S(2k-1,k-1)$ has bipartition classes of sizes $k$ and $2k$, and the bound reads $r(S(2k-1,k-1))\ge4.2k-o(k)$, so $R(T)>4k-1$ for every sufficiently large $k$. The paper states this consequence itself and presents it as a negative answer to the 1982 question of Erdős, Faudree, Rousseau and Schelp, which is the statement of Problem 549: the equality $R(T)=4k-1$ is asserted there for every tree with classes $k$ and $2k$ and every $k$, and one such tree with a larger Ramsey number disproves it. The lower bound $R(T)\ge4k-1$ holds for all these trees by Burr's two colorings, so the paper refutes the upper half of the equality. The disproof is asymptotic: it names no explicit $k$ at which the equality fails. The bound comes from blow-ups of the line graph of $K_7$, which at the ratio $n/m\to2$ need no random sparsification and so are explicit, fed through the paper's reduction of the double-star Ramsey problem to a degree condition.

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

Acceptance. Reviewed: the bound is restated and relied on in the refereed paper of Dubó and Stein (Discrete Mathematics 348 (2025), 114227; Crossref record read), whose introduction (pp. 2--3 of arXiv v2) records that the results of this preprint give $R(S(2m,m))\ge4.2m+o(m)$ and builds its own upper bound around that value; Montgomery, Pavez-Signé and Yan's 2025 preprint on Ramsey numbers of trees calls the 1982 statement "strongly disproved" by it (p. 2); and the site's curator, T. F. Bloom, labels the problem DISPROVED and credits the disproof to the paper in the problem's commentary (page last edited 28 December 2025, read 2026-09-17), a credit independent of the authors. Not refereed: the paper is an arXiv preprint, version 1 of 11 May 2016 (the date this page is named by) and the only version, with no journal version found on 2026-09-17 (the arXiv listing and a Crossref bibliographic query), so refereed is not listed. The refereed Theorem 2.1 of Grossman, Harary and Klawe (Discrete Math. 28 (1979)) gives the failure at every $k\ge4$ by an explicit coloring; it is recorded on its own claim page, Grossman, Harary and Klawe 1979.

Formalization. A Lean development in Boris Alexeev's repository (the formalization link above, added 17 August 2026) formalizes the disproof at $k=16$ from the paper's line-graph construction: a three-fold clique blow-up of the line graph of $K_7$ gives a two-coloring of $K_{63}$ with no monochromatic $S(31,15)$, and $63=4\cdot16-1$. It names Norin, Sun and Zhao as informal authors and Codex and GPT-5.6 Sol as formal authors. This corpus has not built it, so it gives no formalized evidence.

Read depth. Theorem 1.3 and its stated consequence were read clause by clause on the page image of p. 2; the proof (Lemma 3.1, Corollary 3.2 and Theorem 2.4) was read for structure only, the flag algebra certificates behind the paper's upper bounds were not obtained, and nothing is independently reviewed in this corpus. The asymptotic value of $r(S(2k-1,k-1))$, the paper's Question 5.1, is open and is not this problem's question.