On chromaticity of hypergraphs

Let H=(X,E)H=(X,E) be a simple hypergraph and let f(H,λ)f(H,λ) denote its chromatic polynomial. Two hypergraphs H1H1 and H2H2 are chromatic equivalent if f(H1,λ)=f(H2,λ)f(H1,λ)=f(H2,λ). The equivalence class of HH is denoted by 〈H〉〈H〉. Let KK and HH be two classes of hypergraphs. HH is said to be chromatically characterized in KK if for every H∈H∩KH∈H∩K we have 〈H〉∩K=H∩K〈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.