Towards a large set of Steiner quadruple systems
SIAM Journal on Discrete Mathematics
Algorithmic complexity of list colorings
Discrete Applied Mathematics
The monochromatic block number
Proceedings of an international symposium on Graphs and combinatorics
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
Pseudo-chordal mixed hypergraphs
Discrete Mathematics
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Graphs and Hypergraphs
Discrete Applied Mathematics - Special issue: Efficient algorithms
Circular mixed hypergraphs II: the upper chromatic number
Discrete Applied Mathematics
Orderings of uniquely colorable hypergraphs
Discrete Applied Mathematics
Circular mixed hypergraphs II: The upper chromatic number
Discrete Applied Mathematics
Discrete Applied Mathematics - Special issue: Efficient algorithms
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A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring, every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, χ and χ, respectively. A mixed hypergraph is called uniquely colorable if it has precisely one coloring apart from the permutation of colors. We begin a systematic study of uniquely colorable mixed hypergraphs.In particular, we show that every colorable mixed hypergraph can be embedded into some uniquely colorable mixed hypergraph; we investigate the role of uniquely colorable subhypergraphs being separators, study recursive operations (orderings and subset contractions) and unique colorings, and prove that it is NP-hard to decide whether a mixed hypergraph is uniquely colorable.We also discuss the weaker property where the mixed hypergraph has a unique coloring with χ colors and a unique coloring with χ colors, where χ χ. The class of these "weakly uniquely colorable" mixed hypergraphs contains all uniquely colorable graphs in the usual sense.