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Claim. Beck proves that $\hat r(P_n)<900n$ for all sufficiently large $n$, where $\hat r(G)$ is the size Ramsey number, the least number of edges of a graph every $2$-coloring of whose edges contains a monochromatic copy of $G$ (the problem's $\hat R(G)$). The same theorem is recorded on Problem 720's claim page for Beck's paper.

Covers. The statement of Problem 559 for paths, which have maximum degree two: $\hat R(P_n)\le c\,n$ with an absolute constant $c$. Not covered: any other class of bounded-degree graphs. The statement fails in general at maximum degree three, as the pages Rödl and Szemerédi 2000 and Tikhomirov 2022 record.

Dating. The page is dated by the issue month of the journal record (J. Graph Theory 7 (1983), no. 1, March 1983, per the Crossref record); the day in the page name is a placeholder.

Acceptance. Refereed: On size Ramsey number of paths, trees, and circuits. I, J. Graph Theory 7 (1983), no. 1, 115--129. The path bound is attested by Beck's own 1990 sequel (display (1), p. 34, on the source card) and by the introductions of the refereed papers of Javadi, Khoeini, Omidi and Pokrovskiy (2019, p. 2) and of Draganić and Petrova (2025, p. 1). The site's curator, T. F. Bloom, credits Beck with the path case 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. The paper is not held here; the claim rests on the three attestations named above. No proof is covered, and nothing is independently reviewed in this corpus.

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