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
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Complexity of Pattern Coloring of Cycle Systems
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
On Complexity of Colouring Mixed Hypertrees
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
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A mixed hypergraph is a hypergraph with edges classified as of type 1 or type 2. A vertex coloring is strict if no edge of type 1 is totally multicolored, and no edge of type 2 monochromatic. The chromatic spectrum of a mixed hypergraph is the set of integers k for which there exists a strict coloring using exactly k different colors. A mixed hypertree is a mixed hypergraph in which every hyperedge induces a subtree of the given underlying tree. We prove that mixed hypertrees have continuous spectra (unlike general hypergraphs, whose spectra may contain gaps [cf. Jiang et al.: The chromatic spectrum of mixed hypergraphs, submitted]. We prove that determining the upper chromatic number (the maximum of the spectrum) of mixed hypertrees is NP-hard, and we identify several polynomially solvable classes of instances of the problem.