About uniquely colorable mixed hypertrees

A mixed hypergraph is a triple H = (X, C,D) where X is the vertex set and each of C, D is a family of subsets of X, the C-edges and D-edges, respectively. A k-coloring of H is a mapping c : X → [k] such that each C-edge has two vertices with the same color and each D-edge has two vertices with distinct colors. H = (X, C,D) is called a mixed hypertree if there exists a tree T = (X, E) such that every D-edge and every C-edge induces a subtree of T. A mixed hypergraph H is called uniquely colorable if it has precisely one coloring apart from permutations of colors. We give the characterization of uniquely colorable mixed hypertrees.