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LATIN
2010
Springer

Computational Complexity of the Hamiltonian Cycle Problem in Dense Hypergraphs

10 years 6 months ago
Computational Complexity of the Hamiltonian Cycle Problem in Dense Hypergraphs
Abstract. We study the computational complexity of deciding the existence of a Hamiltonian Cycle in some dense classes of k-uniform hypergraphs. Those problems turned out to be, along with the hypergraph Perfect Matching problems, exceedingly hard, and there is a renewed algorithmic interest in them. In this paper we design a polynomial time algorithm for the Hamiltonian Cycle problem for k-uniform hypergraphs with density at least 1 2 + , > 0. In doing so, we depend on a new method of constructing Hamiltonian cycles from (purely) existential statements which could be of independent interest. On the other hand, we establish NP-completeness of that problem for density at least 1 k − . Our results seem to be the first complexity theoretic results for the Dirac-type dense hypergraph classes.
Marek Karpinski, Andrzej Rucinski, Edyta Szymanska
Added 23 Aug 2010
Updated 23 Aug 2010
Type Conference
Year 2010
Where LATIN
Authors Marek Karpinski, Andrzej Rucinski, Edyta Szymanska
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