Unbalanced star-factorisations of complete bipartite graphs.

Abstract

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 su0cient (something already proved in the balanced case where m = n). In this paper, we prove the conjecture for a signi3cant new in3nite family in the unbalanced case where p = 1. As a consequence we prove the general conjecture for complete K1;3-factorisations.