Coloring mixed hypertrees

  • Authors:

  • Daniel Král;Jan Kratochvíl;Andrzej Proskurowski;Heinz-Jürgen Voss

  • Affiliations:

  • Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Prague, Czech Republic;Department of Computer and Information Science, University of Oregon, Eugene, OR;Technische Universität Dresden, Germany

  • Venue:
  • Discrete Applied Mathematics - Special issue: Efficient algorithms
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

A mixed hypergraph is a triple (V, C, D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.