Loose Hamilton cycles in 3-uniform hypergraphs of large minimum degree

We say that a 3-uniform hypergraph has a Hamilton cycle if there is a cyclic ordering of its vertices such that every pair of consecutive vertices lies in a hyperedge which consists of three consecutive vertices. Also, let C-4 denote the 3-uniform hypergraph on 4 vertices which contains 2 edges. We prove that for every epsilon > 0 there is an no such that for every n >= n(0) the following holds: Every 3-uniform hypergraph on n vertices whose minimum degree is at least n/4 + epsilon n contains a Hamilton cycle. Moreover, it also contains a perfect C-4-packing. Both these results are best possible up to the error term epsilon n. (c) 2006 Elsevier Inc. All rights reserved.