Uiversity of Illinois at Chicago
Department of Mathematics, Statistics and Computer Science
1200 W Harrison St.
Chicago, Illinois 60607
United States of America
Abstract: A basic problem in combinatorics is to determine the independence number of a hypergraph. We will consider this question in various contexts. Our results show that the behavior of the independence number of sparse hypergraphs is quite different than the graph case. We will also describe some hypergraph generalizations of the graph Ramsey number $R(3,t)$. Our results address old questions and conjectures of Erdos-Hajnal (1972) and of Ajtai-Erdos-Komlos-Szemeredi (1981).