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    Transitive path decompositions of Cartesian products of complete graphs

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    An HH-decomposition of a graph Γ\Gamma is a partition of its edge set into subgraphs isomorphic to HH. A transitive decomposition is a special kind of HH-decomposition that is highly symmetrical in the sense that the subgraphs (copies of HH) are preserved and transitively permuted by a group of automorphisms of Γ\Gamma. This paper concerns transitive HH-decompositions of the graph Kn□KnK_n \Box K_n where HH is a path. When nn is an odd prime, we present a construction for a transitive path decomposition where the paths in the decomposition are arbitrary large.Comment: 14 pages, 4 figure
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