For n≥30(s+1), every F5-free 3-graph with matching number at most s has at most s⌊(n−s)^2/4⌋ edges, with equality only for the complete 3-partite hypergraph H3(n,s).
Frankl, The Erd˝ os-Ko-Rado theorem is true forn = ckt, Coll
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Hypergraph Tur\'an problem of the generalized triangle with bounded matching number
For n≥30(s+1), every F5-free 3-graph with matching number at most s has at most s⌊(n−s)^2/4⌋ edges, with equality only for the complete 3-partite hypergraph H3(n,s).