Union-Closed Families of Sets

Béla Bollobás

Cambridge and Memphis

Abstract

A family of sets is union-closed if it contains the union of any two of its elements. Much of the interest in union-closed families is due to the notorious union-closed conjecture, which states that for every union-closed family of m sets there is an element in at least m/2 of the sets. In the talk I shall review some of the results about union-closed families, and present some of the results I have proved with Eccles and Balla about the average size of a set in such a family with m members.