On chromaticity of hypergraphs

Let H = (X,E) be a simple hypergraph and let f (H, ) denote its chromatic polynomial. Two hypergraphs H1 and H2 are chromatic equivalent if f (H1, ) = f (H2, ). The equivalence class of H is denoted by 〈H 〉. Let K and H be two classes of hypergraphs.H is said to be chromatically characterized in K if for every H ∈ H ∩K we have 〈H 〉 ∩K=H ∩K. In this paper we prove that uniform hypertrees and uniform unicyclic hypergraphs are chromatically characterized in the class of linear hypergraphs. © 2006 Elsevier B.V. All rights reserved.