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Claim. For $r\ge2$ and $m\ge1$, every graph with $rm$ vertices and minimum degree at least $m(r-1)$ contains $m$ vertex-disjoint copies of $K_r$, the statement of Problem 914. The claimed result is A. Hajnal and E. Szemerédi, Proof of a conjecture of P. Erdős, Combinatorial Theory and its Applications (P. Erdős, A. Rényi and V. T. Sós, eds.), North-Holland (1970), 601--623, a print-only proceedings volume not held, whose statement is known through the refereed papers that restate and reprove it. In the form those papers state, every graph with maximum degree at most $r$ has an equitable $(r+1)$-coloring, a proper coloring whose color classes differ in size by at most one. The problem page's Status support writes the passage between the two forms, an observation made in this corpus: the complement of a graph with $rm$ vertices and minimum degree at least $m(r-1)$ has maximum degree at most $m-1$, an equitable $m$-coloring of the complement has classes of exactly $r$ vertices, and each class is a clique of the graph; conversely $m$ disjoint copies of $K_r$ are the classes of such a coloring. Erdős's conjecture is stated, without its author's name, in his 1967 seminar paper (p. 56), with the cases $r=2$ (Dirac's theorem) and $r=3$ (Corrádi and Hajnal) as known.

Depends on. Nothing in this wiki; the elementary transfer between the two forms is written on the problem page and carries no independent review.

Acceptance. The reviewed evidence is documented acceptance independent of the 1970 paper's authors: the site's curator (T. F. Bloom) credits the proof to the 1970 paper for every $r\ge4$ and labels the problem proved, and Kierstead and Kostochka (Combin. Probab. Comput. 17 (2008), refereed, not held) publish a short proof under the theorem's name. Kierstead, Kostochka, Mydlarz and Szemerédi (Combinatorica 30 (2010), refereed; Theorem 1) state the theorem, attribute it to Hajnal and Szemerédi in 1970 as a conjecture of Erdős, and prove it again, but that paper shares an author, Szemerédi, with the 1970 paper, so it is cited as a restatement and not as independent acceptance; the community database agrees with the site. No evidence that the 1970 proceedings volume was refereed is recorded, so refereed is not listed. The two later proofs have their own claim pages, Kierstead and Kostochka and Kierstead, Kostochka, Mydlarz and Szemerédi. Read depth: the 1970 text was not read; the page name carries its year, and no source read gives the volume's day.