Decomposing complete 3-uniform hypergraphs into Hamiltonian cycles

Using the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph, we continue the investigation of the existence of a decomposition of the complete 3-uniform hypergraph into Hamiltonian cycles began by Bailey and Stevens. We also discuss two extensions of the problem: to the complete 3-uniform hypergraph from which a parallel class of triples has been removed, and to the complete 3-uniform (multi)hypergraph of higher index. We also briefly consider decompositions of 3-uniform hypergraphs into (not necessarily Hamiltonian) cycles and comment on a possible analogue of Alspach’s conjecture for cycle decompositions of the ordinary complete graph.