The multiplicities of centered hypergraphs

Abstract

The multiplicity of a k-uniform hypergraph H and a positive integer n is defined as the smallest number of monochromatic copies of H in any 2-coloring of the hyperedges of the k-uniform complete hypergraph on n vertices. Here, we concentrate on the special case of centered hypergraphs, i.e. hypergraphs containing vertices that are incident to all hyperedges. In particular, we determine the multiplicities of some small 3-uniform centered hypergraphs.