Geodesic
About uniquely colorable mixed hypertrees
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 81-91

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A mixed hypergraph is a triple = (X,,) where X is the vertex set and each of , is a family of subsets of X, the -edges and -edges, respectively. A k-coloring of is a mapping c: X → [k] such that each -edge has two vertices with the same color and each -edge has two vertices with distinct colors. = (X,,) is called a mixed hypertree if there exists a tree T = (X,) such that every -edge and every -edge induces a subtree of T. A mixed hypergraph is called uniquely colorable if it has precisely one coloring apart from permutations of colors. We give the characterization of uniquely colorable mixed hypertrees.
Keywords: colorings of graphs and hypergraphs, mixed hypergraphs, unique colorability, trees, hypertrees, elimination ordering 
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Niculitsa, Angela; Voloshin, Vitaly. About uniquely colorable mixed hypertrees. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 81-91. http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a5/