The mixed hypergraphs

Abstract

We introduce the notion of an anti-edge of a hypergraph, which is a non-overall polychromatic subset of vertices. The maximal number of colors, for which there exists a coloring of a hypergraph using all colors, is called an upper chromatic number of a hypergraph H and denoted by `c(H). The general algorithm for computing the numbers of all colorings of mixed (containing edge and anti-edge sets) hypergraphs is proposed. Some properties of mixed hypergraph colorings and its application are discussed.