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Claim. Theorem 1.2 of the paper: if $t<n/(3k^2)$, every $k$-uniform hypergraph on $n$ vertices with no $t$ pairwise disjoint edges has at most $\binom nk-\binom{n-t+1}{k}$ edges. In the notation of Problem 1020, with $r$ for the uniformity and $k$ for the forbidden number of disjoint edges,

$$f(n;r,k)=\binom nr-\binom{n-k+1}{r}\qquad(n>3r^2k),$$

the conjectured value in that range, the covering family attaining it. The proof uses the shifting method and passes through an asymptotic form of a rainbow-matching strengthening of the conjecture (the paper's Conjecture 1.3), which it also proves in full for $t<n/(3k^2)$. The paper is H. Huang, P.-S. Loh and B. Sudakov, The size of a hypergraph and its matching number, Combin. Probab. Comput. 21 (2012), 442–450, carded at The size of a hypergraph and its matching number.

Covers. The range $n>3r^2k$, which the site records as $n\ge3kr^2$. It improves the order $r^3k$ of Bollobás, Daykin and Erdős 1976 and was improved in turn, to $n>2r^2(k-1)/\log r$ on Frankl, Łuczak and Mieczkowska 2012 and to order $rk$ on Frankl 2013.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper appeared in Combinatorics, Probability and Computing 21 (2012), no. 3, 442–450, after its first posting as arXiv:1107.5544 on 2011-07-27. The site labels the problem FALSIFIABLE, an open label, so its commentary, which credits the range to the paper as [HLS12], is not acceptance and no reviewed is listed. Nothing here rests on this project's own review.