Uniform set systems and their diameters

Abstract

This dissertation examines the existing literature on set systems (or hypergraphs) and conducts an investigation of their (k-1)-overlapping diameters. In the general case of set systems of given diameter, some bounds on the possible sizes are given. We then restrict our focus to acyclic set systems and provide a full classification for simple, connected, acyclic, uniform set systems of each positive diameter, extending some results on trees.