Path and cycle decompositions of complete equipartite graphs: Four parts

Abstract: We show that a complete equipartite graph with four partite sets has an edge-disjoint decomposition into cycles of length if and only if , the partite set size is even, divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least . We also show that a complete equipartite graph with four even partite sets has an edge-disjoint decomposition into paths with edges if and only if divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least . [Copyright &y& Elsevier]