Mixed hypergraphs and other coloring problems Original Research Article

A mixed hypergraph is a triple image where V is the vertex set and image and image are families of subsets of V called image-edges and image-edges, respectively. A proper coloring of a mixed hypergraph image is a coloring of its vertices such that no image-edge is polychromatic and no image-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, image-colorings, image-colorings, locally surjective, locally bijective and locally injective homomorphisms, image-labelings, the channel assignment problem, T-colorings and generalized T-colorings.