On r-cross intersecting families of sets

Abstract

Let [n] = {1,..., n} and denote the family of all k-subsets of [n]. For i = 1, 2,..., r, let Fi⊆. Suppose that F1∩··· ∩Fr≠∅ holds for all Fi∈Fi. We show that ki≤n/2 for all i, then Moreover, equality holds if and only if there is an element x ∈ [n] such that for all i. © 2013 Pushpa Publishing House.