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- W1543959772 abstract "A mixed hypergraph H is a triple (V, C, D) where V is its vertex set and C and D are families of subsets of V, C-edges and D-edges. The degree of a vertex is the number of edges in which it is contained. A vertex coloring of H is proper if each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of H is the set of all k's such that there exists a proper coloring using exactly k colors. The lower (upper) chromatic number of H is the minimum (maximum) number in the feasible set.We prove that it is NP-complete to decide whether the upper chromatic number of mixed hypergraphs with maximum degree two is at least a given k. We present polynomial time algorithms for mixed hypergraphs with maximum degree two to decide their colorability,t o find a coloring using the number of colors equal to the lower chromatic number and we present a 5/3-aproximation algorithm for the upper chromatic number. We further prove that it is coNP-hard to decide whether the feasible set of a given general mixed hypergraph is an interval of integers." @default.
- W1543959772 created "2016-06-24" @default.
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- W1543959772 date "2001-01-01" @default.
- W1543959772 modified "2023-09-27" @default.
- W1543959772 title "Complexity Note on Mixed Hypergraphs" @default.
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- W1543959772 doi "https://doi.org/10.1007/3-540-44683-4_42" @default.
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