On Complexity of Colouring Mixed Hypertrees

Authors:
Daniel Král
Affiliations:
-
Venue:
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Year:
2001

Citing 2
Cited 1

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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, C-edges and D-edges. We demand in a proper colouring that each C-edge contains two vertices with the same colour and each D-edge contains two vertices with different colours. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of that tree. We prove that it is NP-complete to decide existence of a proper k- colouring even for mixed hypertrees with C = D when k is given as part of input. We present a polynomial-time algorithm for colouring mixed hypertrees on trees of bounded degree with fixed number of colours.