Cyclic Hamiltonian cycle systems of the -fold complete and cocktail party graphs

We establish the necessary and sufficient conditions for the existence of a cyclic Hamiltonian cycle system of λ K v and of λ ( K 2 v − I ) . We also consider the existence problem for cyclic Hamiltonian cycle systems of λ K v that are simple, i.e., without repeated cycles, solving it in the case that v is a prime.