In this paper, we prove that cyclic hamiltonian cycle systems of the complete graph minus a 1-factor, K n − I, exist if and only if n ≡ 2, 4(mod 8) and n = 2p α with p prime and α ≥ 1.
Let G of order n be the vertex-disjoint union of an even and an odd cycle. It is known that there exists a G-decomposition of K v for all v ≡ 1 (mod 2n). We use an extension of the Bose construction for Steiner triple systems and a recent result on the Oberwolfach Problem for 2-regular graphs with two components to show that there exists a G-decomposition… (More)
In this paper, we settle Alspach's problem in the case of Hamilton cycles and 5-cycles; that is, we show that for all odd integers n ≥ 5 and all nonnegative integers h and t with hn + 5t = n(n − 1)/2, the complete graph K n decomposes into h Hamilton cycles and t 5-cycles and for all even integers n ≥ 6 and all nonnegative integers h and t with hn + 5t =… (More)
In this paper, we prove that directed cyclic hamiltonian cycle systems of the complete symmetric digraph, K * n , exist if and only if n ≡ 2 (mod 4) and n = 2p α with p prime and α ≥ 1. We also show that directed cyclic hamiltonian cycle systems of the complete symmetric digraph minus a set of n/2 vertex-independent digons, (K n − I) * , exist if and only… (More)