Uniform hypergraphs with many edge‐colorings avoiding a fixed rainbow expanded complete graph

Abstract

AbstractFor fixed positive integers and , and a fixed ‐uniform hypergraph , we look for ‐vertex hypergraphs that admit the maximum number of ‐edge‐colorings with the property that there is no copy of for which all hyperedges are assigned different colors. We consider , the ‐uniform expanded complete graph, and we prove that the Turán hypergraph , the balanced ‐partite ‐uniform hypergraph on vertices, is the only extremal configuration for any and large .