On cyclic Hamiltonian decompositions of complete k-uniform hypergraphs

A decomposition C = {C-1, C-2, ..., C-h} of the complete k-uniform hypergraph K-n(k) of order n is called cyclic Hamiltonian if each C-i is an element of C, i is an element of {1, 2, ..., h), is a Hamiltonian cycle in K-n(k) and there exists a permutation sigma of the vertex set of K-n(k) having exactly one cycle in its cycle decomposition such that for every cycle C-i is an element of C its set of edges coincides with an orbit of when acting on the edge set of K-n(k). In this paper it is shown that K-n(k) admits a cyclic Hamiltonian decomposition if and only if n and k are relatively prime and lambda = min{d > 1 : d vertical bar n} > n/k. (C) 2014 Elsevier B.V. All rights reserved.