Packing hamilton cycles in random and pseudo-random hypergraphs

We say that a k-uniform hypergraph C is a Hamilton cycle of type `, for some 1 ≤ ` ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges Ei−1, Ei in C (in the natural ordering of the edges) we have |Ei−1 \ Ei| = `. We prove that for k/2 < ` ≤ k, with high probability almost all edges of the random k-uniform hypergraph H(n, p, k) with p(n) log n/n can be decomposed into edge-disjoint type ` Hamilton cycles. A slightly weaker result is given for ` = k/2. We also provide sufficient conditions for decomposing almost all edges of a pseudo-random k-uniform hypergraph into type ` Hamilton cycles, for k/2 ≤ ` ≤ k. For the case ` = k these results show that almost all edges of corresponding random and pseudo-random hypergraphs can be packed with disjoint perfect matchings.