On the Maximum Number of Edges in a Hypergraph with a Unique Perfect   Matching
  In this note, we determine the maximum number of edges of a $k$-uniform hypergraph, $k\ge 3$, with a unique perfect matching. This settles a conjecture proposed by Snevily. 
Deepak Bal, Andrzej Dudek, Zelealem B. Yilma
math.CO