Towards a large set of Steiner quadruple systems
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
Upper chromatic number of Steiner triple and quadruple systems
Proceedings of the international conference on Combinatorics '94
Strict colouring for classes of Steiner triple systems
Discrete Mathematics - Special issue on Graph theory
Graph classes: a survey
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
About the upper chromatic number of a co-hypergraph
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Uniquely colorable mixed hypergraphs
Discrete Mathematics
Mixed hypergraphs with bounded degree: edge-coloring of mixed multigraphs
Theoretical Computer Science - Mathematical foundations of computer science
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Hi-index | 0.01 |
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.