Packing Tight Hamilton Cycles in Uniform 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 Ei−1, Ei in C (in the natural ordering of the edges) we have |Ei−1 \ Ei | = ℓ. We define a class of (ε, p)-regular hypergraphs, that includes random hypergraphs, for which we can prove the existence of a decomposition of almost all edges into type ℓ Hamilton cycles, where ℓ < k/2.