Hamilton l-cycles in uniform hypergraphs

We say that a k-uniform hypergraph C is an l-cycle if there exists a cyclic ordering of the vertices of C such that every edge of C consists of k consecutive vertices and such that every pair of consecutive edges (in the natural ordering of the edges) intersects in precisely l vertices. We prove that if 1 <= l < k and k - l does not divide k then any k-uniform hypergraph on n vertices with minimum degree at least n/[k/k-l] (k-l) + o(n) contains a Hamilton l-cycle. This confirms a conjecture of Han and Schacht. Together with results of Rodl, Rucinski and Szemeredi, our result asymptotically determines the minimum degree which forces an l-cycle for any l with 1 <= l < k. (C) 2010 Elsevier Inc. All rights reserved.