Discussiones Mathematicae Graph Theory 20 (2000 ) 293–301 CHROMATIC POLYNOMIALS OF HYPERGRAPHS Mieczys law Borowiecki Institute of Mathematics, Technical University of Zielona G´ora Podg´ orna 50, 65–246 Zielona G´ora, Poland e-mail: m.borowiecki@im.pz.zgora.pl and Ewa  Lazuka Department of Applied Mathematics, Technical University of Lublin Bernardy´ nska 13, 20–950 Lublin, Poland e-mail: elazuka@antenor.pol.lublin.pl Abstract In this paper we present some hypergraphs which are chromatically characterized by their chromatic polynomials. It occurs that these hy- pergraphs are chromatically unique. Moreover we give some equalities for the chromatic polynomials of hypergraphs generalizing known results for graphs and hypergraphs of Read and Dohmen. Keywords: chromatic polynomial, chromatically unique hypergraphs, chromatic characterization. 2000 Mathematics Subject Classification: 05C15. 1. Introduction A simple hypergraph H =(V, E ) consists of a finite non-empty set V of vertices and a family E of edges which are distinct non-empty subsets of V of the cardinality at least 2. An edge of cardinality h is called h-edge. H is h-uniform if |e| = h for each edge e ∈E , i.e., H contains only h-edges. A hypergraph, no edge of which is a subset of another is called Sperner. If λ ∈N ,a λ-coloring of H is such a function f : V (H ) →{1, 2,...,λ} that for each edge e of H there exist x, y in e for which f (x) = f (y). The number of λ-colorings of H is given by a polynomial f (H, λ) of degree |V (H )| in λ, called the chromatic polynomial of H .