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Claim. For every graph $H$ with $m$ edges and no isolated vertices, if $m$ is large enough, then

$$R(C_5,H)\le2m+2,$$

the case $k=5$ of Problem 570, since $\lfloor(5-1)/2\rfloor=2$. The site's reference record attributes it to C. J. Jayawardene, Ramsey numbers related to small cycles. University of Memphis (1999), with no theorem number; Cambie, Freschi, Morawski, Petrova and Pokrovskiy (2026), p. 2, write that the case $k=5$ was resolved by Jayawardene and cite the thesis as their reference [16], again without a theorem number. The locator and the statement come from the later preprint of Cambie and Freschi (arXiv:2606.11174v1, proof of Lemma 4, p. 2; library home cambie_2026_general_bound_r_c_k_h), which cites Theorems 4.1, 4.5 and 4.7 of the thesis for the cycle lengths $4$, $5$ and $6$ and reports, for $k=5$, that $R(C_5,H)\leq2m+2$ for every connected graph $H$ with $m$ edges on at least four vertices, with no largeness condition on $m$ (printed there as an equality; the lemma uses only the upper bound, which is all that is recorded here). A comment of 9 September 2025 in the site's discussion thread (linked above), by the first author of both preprints, also places the result at Theorem 4.5 and credits the observation to Pokrovskiy.

Covers. The case $k=5$. As reported by Cambie and Freschi, Theorem 4.5 of the thesis gives $R(C_5,H)\leq2m+2$ for every connected $H$ on at least four vertices and every $m$; the eventual bound for every $H$ without isolated vertices, which the problem asks, is reported by Cambie, Freschi, Morawski, Petrova and Pokrovskiy and credited by the site. Neither statement is checked against the thesis.

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

Acceptance. Reviewed: the site's curator, T. F. Bloom, records the case $k=5$ as proved by Jayawardene in the problem's commentary (its key [Ja99]; page last edited 16 January 2026, accessed 2026-09-08 for the problem page), and the five authors of the 2026 preprint, who prove the remaining odd cases, accept the thesis result as settling $k=5$ and build their account of the question on it. A thesis is examined, not refereed in a journal, and no journal publication of the result is known, so no refereed evidence is listed.

Dating and read depth. The thesis is not held: the searches of 2026-09-08 (title, author, catalog and web queries, including ProQuest and WorldCat, and the author's University of Colombo page) recovered its identity but no copy and no theorem page, and no URL for it is known to this corpus, so the links above are the site's page and the thread comment. The page is dated by the thesis year, with a placeholder day. Everything attributed to the thesis here is second-hand: the theorem numbers and the connected-case statement from Cambie and Freschi's Lemma 4, in arXiv v1; the credit for the eventual bound from the 2026 preprint of Cambie, Freschi, Morawski, Petrova and Pokrovskiy (p. 2) and the site's record; and the thread comment as corroboration. Reopening condition: a copy of the thesis read at Theorem 4.5.