Enumeration of Maximum Acyclic Hypergraphs

Abstract

Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be $$ {\left( {\begin{array}{*{20}c} {n} \\ {{r - 1}} \\ \end{array} } \right)}{\left( {n{\left( {r - 1} \right)} - r^{2} + 2r} \right)}^{{n - r - 1}} . $$