Introduction to algorithms
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Towards a large set of Steiner quadruple systems
SIAM Journal on Discrete 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
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
On the Approximation Properties of Independent Set Problem in Degree 3 Graphs
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Discrete Applied Mathematics - Special issue: Efficient algorithms
Discrete Applied Mathematics - Special issue: Efficient algorithms
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A mixed hypergraph H 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). The degree of a vertex is the number of edges in which it is contained. A vertex coloring of H is proper if each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of H is the set of all k's such that there exists a proper coloring using exactly k colors. The lower (upper) chromatic number of H is the minimum (maximum) number in the feasible set.We restrict our attention to mixed hypergraphs with maximum degree two; those with maximum degree three are not simpler than general ones. Mixed hypergraphs with maximum degree two were suggested as an interesting subclass of mixed hypergraphs in Voloshin (Austral. J. Combin. 11 (1995) 25-45). We prove that feasible sets of mixed hypergraphs with maximum degree two are intervals. We present a linear time algorithm for determining the lower chromatic number, a linear 5/3-approximation algorithm and a polynomial 3/2-approximation algorithm for the upper chromatic number. We prove that there is no PTAS for the upper chromatic number unless P = NP.