On the Maximum Number of Edges in a Hypergraph with Given Matching   Number
  The aim of the present paper is to prove that the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is max{\binom(3s+2,3), \binom(n,3) - \binom(n-s,3)} for all n,s, n >= 3s+2. 
Peter Frankl
math.CO