Motivated by the famous theorem of Helly on convex sets of ℝd, 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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics