Results on intersecting families of subsets, a survey

Abstract

The underlying set will be {1, 2, . . . , n}. The family of all k-element subsets of [n] is denoted by ( [n] k ) . Its subfamilies are called uniform. A family F of some subsets of [n] is called intersecting if F ∩ G 6= ∅ holds for every pair F,G ∈ F . The whole story has started with the seminal paper of Erdős, Ko and Rado [7]. Their first observation was that an intersecting family in 2 can contain at most one of the complementing pairs, therefore the size of an intersecting family cannot exceed the half of the number of all subsets of [n].