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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)
A classic theorem of Veblen states that a connected graph G has a cycle decomposition if and only if G is Eulerian. The number of odd cycles in a cycle decomposition of an Eulerian graph G is therefore even if and only if G has even size. It is conjectured that if the minimum number of odd cycles in a cycle decomposition of an Eulerian graph G with m edges(More)
A k-extended Skolem-type 5-tuple difference set of order t is a set of t 5-tuples 5t+1}\{k}. In this talk, we will give necessary and sufficient conditions on t and k for the existence of a k-extended Skolem-type 5-tuple difference set of order t. We also consider hooked k-extended Skolem-type 5-tuple difference sets of order t and provide necessary and(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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