Abstract
There are simple arithmetic conditions necessary for the complete bipartite graph Km,n to have a complete factorization by subgraphs that are made up of disjoint copies of Pk, the path on k vertices. Using a difficult construction, Du and Wang showed that these conditions are also sufficient, but left open the corresponding conjecture for complete multigraphs λKm,n. In this paper we reformulate the problem to make it more tractable in individual cases. Using this new approach we prove the multigraph conjecture; our proof yields a much simpler proof for the original case λ=1.
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