A Dirac-type theorem for 3-uniform hypergraphs

A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which every three consecutive vertices form an edge. In this paper we prove an approximate and asymptotic version of an analogue of Dirac's celebrated theorem for graphs: for each gamma > 0 there exists no such that every 3-uniform hypergraph on n >= n(0) vertices, in which each pair of vertices belongs to at least (1/2 + gamma)n edges, contains a Hamiltonian cycle.