Mixed hypergraphs and other coloring problems

A mixed hypergraph is a triple (V,C,D)(V,C,D) where V   is the vertex set and CC and DD are families of subsets of V   called CC-edges and DD-edges, respectively. A proper coloring of a mixed hypergraph (V,C,D)(V,C,D) is a coloring of its vertices such that no CC-edge is polychromatic and no DD-edge is monochromatic. We show that mixed hypergraphs can be used to efficiently model several graph coloring problems including homomorphisms of simple graphs and multigraphs, circular colorings, (H,C,⩽K)(H,C,⩽K)-colorings, (H,C,K)(H,C,K)-colorings, locally surjective, locally bijective and locally injective homomorphisms, L(p,q)L(p,q)-labelings, the channel assignment problem, T-colorings and generalized T-colorings.