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Transitive path decompositions of Cartesian products of complete graphs
An -decomposition of a graph is a partition of its edge set into
subgraphs isomorphic to . A transitive decomposition is a special kind of
-decomposition that is highly symmetrical in the sense that the subgraphs
(copies of ) are preserved and transitively permuted by a group of
automorphisms of . This paper concerns transitive -decompositions of
the graph where is a path. When 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