Complete bipartite factorisations of \(K _{n,n}\)
type: Item
instance of: scholarly article
title: Complete bipartite factorisations of \(K _{n,n}\)
zbMATH Open document ID: 1020.05057
DOI: 10.1016/S0012-365X(02)00819-1
author: Nigel Martin
published in: Discrete Mathematics
publication date: 2003-06-09T00:00:00Z
review text: 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.
reviewed by: Ratnakaram Nava Mohan
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1924777
zbMATH Keywords: bipartite graph
zbMATH Keywords: factorisation
MaRDI profile type: Publication
cites work: \(K_{1,p^2}\)-factorization of complete bipartite graphs
cites work: Complete bipartite factorisations by complete bipartite graphs
cites work: Balanced bipartite graphs may be completely star-factored
cites work: \(P_ 3\)-factorization of complete bipartite graphs
cites work: Q3976650
cites work: On \(K_{1,k}\)-factorizations of a complete bipartite graph
full work available at URL: s0012-365x(02)00819-1
OpenAlex ID: W2066387102
description: scientific article; zbMATH DE number 1924777