Quasi‐random hypergraphs

A large equivalence class of properties shared by most hypergraphs, including so-called random hyper graphs, are described, which shows that many global properties of hyperGraphs are actually consequences of simple local conditions.

Abstract

Abstract We introduce an equivalence class of varied properties for hypergraphs. Any hypergraph possessing any one of these properties must of necessity possess them all. Since almost all random hypergraphs share these properties, we term these properties quasi‐random. With these results, it becomes quite easy to show that many natural explicit constructions result in hypergraphs which imitate random hypergraphs in a variety of ways.