Helly property in finite set systems

Abstract

Motivated by the famous theorem of Helly on convex sets of R d , a finite set system F is said to have the d-dimensional Helly property if in every subsystem F ′ ⊂ F whose members have an empty intersection there are at most d + 1 sets with an empty intersection again. We present several results and open problems concerning extremal properties of set systems satisfying the Helly property.