Cyclic Hamiltonian cycle systems of the complete graph Original Research Article

We prove that there exists a cyclic Hamiltonian k-cycle system of the complete graph if and only if k is odd but k≠15 and pα with p prime and α>1. As a consequence we have the existence of a cyclic k-cycle system of the complete graph on km vertices for any pair (k,m) of odd integers with k as above but (k,m)≠(3,3).