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Claim. V. Chvátal, Tree-complete graph Ramsey numbers, J. Graph Theory 1 (1977), no. 1, 93, proves that for every tree $T$ on $n$ vertices and every $m\ge1$

$$R(T,K_m)=(m-1)(n-1)+1.$$

The one-page note is not held by this corpus; the statement is taken from its restatements by Burr and Erdős (Utilitas Math. 9 (1976), p. 248, in the proof of their Theorem 2.1: for any tree $T$ on $m$ points, $r(T,K_n)=(m-1)(n-1)+1$), by Erdős, Faudree, Rousseau and Schelp (Combinatorica 5 (1985), p. 311) and by Li (arXiv:2606.23659v1, p. 1), which agree.

Covers. The case $m_1=\dots=m_k=1$ of Problem 550, for every $n$: then $G=K_k$, $R(T,K_{1,1})=R(T,K_2)=n$, and both sides of the inequality equal $(k-1)(n-1)+1$. Every case with a class of size at least 2 is outside it.

Depends on. Nothing in this wiki; the theorem and its proof are the paper's own.

Acceptance. Refereed: the note is a journal publication in the Journal of Graph Theory, volume 1, number 1 (March 1977), the refereed evidence; the issue carries no day, so this page is dated to the first day of that month. The site's curator credits the theorem in the problem's commentary, but the site's label OPEN (LEAN) settles neither the problem nor a declared part of it, so reviewed is not listed.