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Claim. Theorem 1 (p. 168) of the paper on the library's [[../library/ramsey_theory/gerencser_1967_ramsey_type_problems/_index|source card]], [[../library/ramsey_theory/gerencser_1967_ramsey_type_problems/theorem_1|Theorem 1]]: writing $g(k,l)$ for the least number of vertices of a graph $G$ that forces a path of length $k$ in $G$ or one of length $l$ in its complement, $g(k,l)=k+[(l+1)/2]$ for $k\ge l$. A path of length $k$ has $k+1$ vertices, so the diagonal case $k=l=n-1$ gives the path $P_n$ on $n$ vertices the Ramsey number

$$R(P_n)=n-1+\lfloor n/2\rfloor,$$

which is at most $2n-2$ for every $n\ge2$. The site's commentary on the problem states the same value for paths and credits the paper.

Covers. The corrected Statement of Problem 547 for every path $P_n$, $n\ge2$. 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 paper's own theorem.

Acceptance. Refereed: L. Gerencsér and A. Gyárfás, On Ramsey-type problems, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 10 (1967), 167--170, a journal of the Eötvös University; the volume is dated 1967, and this page's date is the first day of that year. No reviewed evidence is listed: the site's label DECIDABLE settles neither the problem nor any part of it.