Unbalanced star-factorisations of complete bipartite graphs Original Research Article

There are simple arithmetic conditions necessary for the complete bipartite graph Km,n to have a complete factorisation by subgraphs which are made up of disjoint copies of Kp,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 unbalanced case where p=1. As a consequence we prove the general conjecture for complete K1,3-factorisations.