Complete bipartite factorisations of \(K _{n,n}\)
This paper is a continuation of the earlier work examining factorization of complete bipartite graphs of the form \(K_{n,n}\) by factors whose components are copies of \(K_{p,q}\) for given fixed \(p< q\). It follows from the basic work done in [\textit{N. Martin}, Discrete Math. 167/168, 461-480 (1997; Zbl 0878.05066)] that there are simple arithmetic conditions which are necesary for such factorizations to exist. Early investigations in this area concentrated on star factorizations. This paper sets out a general strategy for showing that these conditions are also sufficient for \(p\), \(q\) coprime and odd which is extending the work of earlier papers where the case \(p=1\) was solved. In this paper the author uses the strategy to solve the sufficiency problem for given \(p\) whenever \(q\) is sufficiently large.
scientific article; zbMATH DE number 1924777