---

Claim. Let $j\ge2$. For every graph $H$ with $m$ edges and no isolated vertices, if $m$ is large enough in terms of $j$, then

$$R(C_{2j},H)\le2m+j-1.$$

Since $\lfloor(2j-1)/2\rfloor=j-1$, this is the bound of Problem 570 for every even $k\ge4$, with the problem's sufficiently-large threshold. The same paper poses the question as its Question 5 (p. 399), for every $m$ and without the eventual qualification; the site's formulation carries the threshold. The result is paged as Corollary 4 of the library's source card, which also records the matching lower bound for a matching $H$ that makes the corollary sharp.

Covers. Every even $k\ge4$, for all sufficiently large $m$ in terms of $k$. Nothing about odd cycle lengths.

Depends on. Nothing in this wiki; the result rests on the cited paper alone.

Acceptance. Reviewed: the site's curator, T. F. Bloom, labels the problem proved and credits the even case to this paper (its key [EFRS93]; page last edited 16 January 2026, accessed 2026-09-08 for the problem page), and the 2026 preprint of Cambie, Freschi, Morawski, Petrova and Pokrovskiy records on p. 2 that the paper verified the question for even $k$. Refereed: P. Erdős, R. J. Faudree, C. C. Rousseau and R. H. Schelp, Ramsey size linear graphs, Combin. Probab. Comput. 2 (1993), no. 4, 389--399, received 12 March 1993 and printed in the December 1993 issue (Crossref), the month this page is dated by; the day is a placeholder.

Read depth. The statement, the range $j\ge2$, the formula and the sharpness construction were checked (printed p. 396); the proof, an immediate consequence of the paper's Theorem 6 (pp. 396--397), was not checked. Nothing is independently reviewed in this corpus.