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On K1,k-factorizations of a complete bipartite graph

✍ Scribed by Hong Wang

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
311 KB
Volume
126
Category
Article
ISSN
0012-365X

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✦ Synopsis

We present a necessary condition for a complete bipartite graph K,., to be K,.,-factorizable and a sufficient condition for K,,, to have a K,,,-factorization whenever k is a prime number. These two conditions provide Ushio's necessary and sufficient condition for K,,, to have a K,,,-factorization.

Theorem 1.1. Let k( > l), m and n be positive integers. If K,,. has a KI,k-factorization then m< kn, n< km, kn-mrkm-n-O(mod(k2-1)) and (kn-m)(km-n)=O (modk(k'-l)(m+n)).

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