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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 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)
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