| Summary: | Thesis (M.Sc.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics Includes bibliographical references (leaves [100]-102). A T (G ) triple is formed by taking a graph G and replacing every edge with a 3-cycle, where all of the new vertices are distinct from all others in G . An edge-disjoint decomposition of 3Kn into T (G ) triples is called a T ( G ) triple system of order n . If we can decompose Kn into copies of a graph G , such that we can form a T (G ) triple from each graph in the decomposition and produce a partition of the edges of 3K n , then the resulting T (G ) triple system is called perfect. -- We give necessary and sufficient conditions for the existence of perfect T (G ) triple systems when G is a matching with λ edges, which we denote by ∪λ P2 . We then give cyclic perfect decompositions of 3 Kn into T (∪λ P2 ) triples for all n ≡ 1 (mod 2λ) when λ is even (except for n = 4λ + 1 when λ > 8) as well as completely solve the case λ = 3.
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