Cyclic hamiltonian cycle systems of the complete graph minus a 1-factor

In this paper, we prove that cyclic hamiltonian cycle systems of the complete graph minus a 1-factor, Kn-IKn-I, exist if and only if n≡2,4(mod8) and n≠2pαn≠2pα with p   an odd prime and α⩾1α⩾1.