Some properties of ordered hypergraphs

Abstract

In this paper, all graphs and hypergraphs are finite. Forany ordered hypergraph $H$, the associated graph $G_H$ of $H$ isdefined. Some basic graph-theoretic properties of $H$ and $G_H$ arecompared and studied in general and specially via the largestnegative real root of the clique polynomial of $G_H$. It is alsoshown that any hypergraph $H$ contains an ordered subhypergraphwhose associated graph reflects some graph-theoretic properties of$H$. Finally, we define the depth of a hypergraph $H$ and introducea constructive algorithm for coloring of $H$.