On chromaticity of hypergraphs

Abstract

Let H = ( X , E ) be a simple hypergraph and let f ( H , λ ) denote its chromatic polynomial. Two hypergraphs H 1 and H 2 are chromatic equivalent if f ( H 1 , λ ) = f ( H 2 , λ ) . 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.