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Claim. The paper proves Erdős's conjectured formula for the maximum number of edges of a $3$-uniform hypergraph on $n$ vertices without a matching of size $s$ (the paper's abstract writes $s$ for the forbidden matching size) for every $s\ge1$ and $n\ge4s$. In the notation of Problem 1020, where $k$ is the forbidden number of disjoint edges,

$$f(n;3,k)=\max\left(\binom{3k-1}{3},\binom n3-\binom{n-k+1}{3}\right) \qquad(n\ge4k).$$

The paper is P. Frankl, V. Rödl and A. Ruciński, On the maximum number of edges in a triple system not containing a disjoint family of a given size, Combin. Probab. Comput. 21 (2012), 141–148.

Covers. The case $r=3$ for $n\ge4k$, as the site records it. The rest of the case $r=3$ was settled for $n$ large on Łuczak and Mieczkowska 2014 and for every $n$ on Frankl 2017.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper appeared in Combinatorics, Probability and Computing 21 (2012), no. 1–2, 141–148, published online on 2012-02-02, the page's date. The site labels the problem FALSIFIABLE, an open label, so its commentary, which credits the range to the paper as [FRR12], is not acceptance and no reviewed is listed. Nothing here rests on this project's own review.