Non-trivial 3-wise intersecting uniform families

Abstract

A family of k-element subsets of an n-element set is called 3-wise intersecting if any three members in the family have non-empty intersection. We determine the maximum size of such families exactly or asymptotically. One of our results shows that for every ϵ>0 there exists n0 such that if n>n0 and 25+ϵ<kn<12−ϵ then the maximum size is 4(n−4k−3)+(n−4k−4).