Complete bipartite factorisations of Kn,n.

Abstract

We continue the study of complete factorisations of complete bipartite graphs of the form Kn,n by factors whose components are copies of Kp,q for given, fixed, p<q. There are simple Basic Arithmetical Conditions which are necessary for such to exist. This paper sets out a general strategy for showing that these conditions are also sufficient for p and q coprime and odd extending work of earlier papers where the case p=1 was solved. Here we use the strategy to solve the sufficiency problem for given p whenever q is sufficiently large.