SOME PROPERTIES OF ORDERED HYPERGRAPHS

Abstract. In this paper, all graphs and hypergraphs are finite. For any ordered hypergraph H, the associated graph GH of H is defined. Some basic graph-theoretic properties of H and GH are compared and studied in general and specially via the largest negative real root of the clique polynomial of GH. It is also shown that any hypergraph H contains an ordered subhypergraph whose associated graph reflects some graph-theoretic properties of H. Finally, we define the depth of a hypergraph H and introduce a constructive algorithm for coloring of H. 1