Kenneth Roblee, Vitaly Voloshin
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 proper k-coloring of H is a mapping c:→[k] such that each C-edge has two vertices with a common color and each D-edge has two vertices with distinct colors. Upper chromatic number is the maximum number of colors that can be used in a proper coloring. A mixed hypergraph H is called a mixed hypertree if there exists a host tree on the vertex set X such that every edge (C- or D-) induces a connected subtree of this tree. We show that if a mixed hypertree can be decomposed into interval mixed hypergraphs then the upper chromatic number can be computed using the same formula.
K. Roblee, V. Voloshin
Department of Mathematics and Physics,
Troy, Alabama, USA
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