Matchings in hypergraphs

Combinatorics Seminar
Friday, April 20, 2012 - 3:05pm
1 hour (actually 50 minutes)
Skiles 005
Emory University and Adam Mickiewicz University, Poznan
Let H_k(n,s) be a k-uniform hypergraphs on n vertices in which the largest matching has s edges. In 1965 Erdos conjectured that the maximum number of edges in H_k(n,s) is attained either when H_k(n,s) is a clique of size ks+k-1, or when the set of edges of H_k(n,s) consists of all k-element sets which intersect some given set S of s elements. In the talk we prove this conjecture for k = 3 and n large enough. This is a joint work with Katarzyna Mieczkowska.