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.

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Marek Karpinski, Andrzej Rucinski, Edyta Szymanska
• Keywords: Hamiltonian Cycle Problem, Hamiltonian Cycles, Information Management, K-uniform Hypergraphs, LATIN 2010