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Claim. Corollary 11 states: "For any fixed $r\ge2$, the induced size-Ramsey number $r_e^{\mathrm{ind}}(C^\ell)$ of the $\ell$-cycle $C^\ell$ is at most $c\ell$, where $c=c_r>0$ is a constant that depends only on $r$." An induced monochromatic copy is in particular a monochromatic copy, so in two colors $\hat r(C_\ell)=O(\ell)$. The corollary follows from Theorem 10, a graph of linear size in which every $r$-coloring of the edges has induced monochromatic cycles of every length between $B\log n$ and $bn$. The results are paged at Theorem 10 and Corollary 11 of the library's source card, whose page numbers are the authors' preprint's (Corollary 11 on p. 11), not the journal's. The same result is recorded on Problem 720's claim page for the paper.

Covers. The statement of Problem 559 for cycles, which have maximum degree two: $\hat R(C_n)\le c\,n$ with an absolute constant $c$. Not covered: other graphs. Explicit constants came later, on the page Javadi, Khoeini, Omidi and Pokrovskiy 2017.

Dating. The page is dated by the issue month of the journal record (Combin. Probab. Comput. 4 (1995), no. 3, September 1995, per the Crossref record); the day in the page name is a placeholder.

Acceptance. Refereed: The induced size-Ramsey number of cycles, Combin. Probab. Comput. 4 (1995), no. 3, 217--239. The site's curator, T. F. Bloom, credits the cycle case to this paper 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 10 and Corollary 11 (preprint p. 11); 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.