Packing hamilton cycles in random and pseudo-random hypergraphs

We say that a k -uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ 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 E _i-1,E _i in C (in the natural ordering of the edges) we have |E _i-1 / E _i| = ℓ. We prove that for k/2 < ℓ ≤ k, with high probability almost all edges of the random k -uniform hypergraph H(n,p,k) with p(n) ≫ log ²n/n can be decomposed into edge-disjoint type ℓ Hamilton cycles. A slightly weaker result is given for ℓ = k/2. We also provide sufficient conditions for decomposing almost all edges of a pseudo-random k -uniform hypergraph into type ℓ Hamilton cycles, for k/2 ≤ ℓ ≤ k. For the case ℓ = k these results show that almost all edges of corresponding random and pseudo-random hypergraphs can be packed with disjoint perfect matchings. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012