Unbalanced bipartite factorizations of complete bipartite graphs.

Abstract

We construct a new infinite family of factorizations of complete bipartite graphs by factors all of whose components are copies of a (fixed) complete bipartite graph $K_{p,q}. There are simple necessary conditions for such factorizations to exist. The family constructed here demonstrates sufficiency in many new cases. In particular, the conditions are always sufficient when $q=p+1$.