The Minimum Number of Edges in Uniform Hypergraphs with Property O
  An oriented k-uniform hypergraph (a family of ordered k-sets) has the ordering property (or Property O) if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. We find bounds on the minimum number of edges in a hypergraph with Property O. 
Dwight Duffus, Bill Kay and Vojtech Rodl
math.CO