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There are simple arithmetic conditions necessary for the complete bipartite graph K m,n to have a complete factorisation by subgraphs which are made up of disjoint copies of K p,q . It is conjectured that these conditions are also sufficient (something already proved in the balanced case where m=n). In this paper, we prove the conjecture for a significant new infinite family in the...
We study complete K p,q -factorisations of K m,n . Simple necessary conditions are found and we conjecture that these conditions are also sufficient. A general construction is given to find infinite families of factorisations proving the conjecture in many cases. The conjecture is proved for K 1,q -factorisations of K n,n except...
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