On a problem of Erdos and Moser
On a problem of Erdos and Moser

Alex Scott, Oxford University
Fine Hall 224
A set A of vertices in an runiform hypergraph H is ``covered'' in H if, for every (r−1)set B contained in A, the set B+{u} is an edge of H. Erdos and Moser (1970) determined the minimum number of edges in a graph on n vertices such that every kset is covered. We extend this result to runiform hypergraphs on sufficiently many vertices, and determine the extremal hypergraphs. We also address the problem for directed graphs. Joint work with Bela Bollobas.