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Claim. Theorem 1.1: for sufficiently large integers $n_1,\dots,n_t$, of which $t_e$ are even and $t_o$ odd, with $n=\max_in_i$, $c=82\times35^{2^{t_o}-2}\times81^{t_e}$ and $n_i\ge2\lceil\log(nc)\rceil+2$ for every $i$,

$$\hat R(C_{n_1},\dots,C_{n_t})\le(\ln c+1)\,c^2\,n,$$

proved by showing that a suitable Erdős--Rényi random graph is almost surely Ramsey for the cycles, without the regularity lemma. In two colors the paper gives $\hat R(C_n,C_n)\le10^6\times cn$ for large $n$ (abstract), with $c=843$ for even $n$ from its Theorem 3.6 (p. 12) and $c=113482$ for odd $n$ from its Theorem 3.4 (p. 11). The theorem is paged at Theorem 1.1 of the library's source card, whose locators are those of arXiv v1 (25 January 2017), the date this page is named by.

Covers. The statement of Problem 559 for cycles, with explicit constants; a second proof of the case first proved on the page Haxell, Kohayakawa and Łuczak 1995. Not covered: other graphs.

Acceptance. Refereed: On the size-Ramsey number of cycles, Combin. Probab. Comput. 28 (2019), no. 6, 871--880, published online 17 July 2019 (the Crossref record). The site's curator, T. F. Bloom, credits the paper with an alternative proof for cycles with better constants in the problem's commentary, but the DISPROVED label settles the problem in the negative and credits no positive sub-claim, so the credit is not reviewed evidence.

Read depth. Claims checked: Theorem 1.1 and the abstract (pp. 1--2) and the two-color consequences of Theorems 3.4 and 3.6 (pp. 11--12) in arXiv v1; no proof is covered, and nothing is independently reviewed in this corpus. The journal text is not compared with the preprint.

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