On Erdos' extremal problem on matchings in hypergraphs
  In 1965 Erd\H{o}s conjectured that the number of edges in k-uniform hypergraphs on n vertices in which the largest matching has s edges is maximized for hypergraphs of one of two special types. We settled this conjecture in the affirmative for k=3 and n is large enough. 
Tomasz Luczak, Katarzyna Mieczkowska
math.CO