On K p,q -factorization of complete bipartite multigraphs

Mingchao Li () and Jian Wang ()
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Mingchao Li: Department of Mathematics Soochow University
Jian Wang: Nantong Vocational University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 2, 221-231

Abstract: Abstract Let λK m,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A K p,q -factorization of λK m,n is a set of edge-disjoint K p,q -factors of λK m,n which partition the set of edges of λK m,n . When p = 1 and q is a prime number, Wang, in his paper [On K 1,q -factorization of complete bipartite graph, Discrete Math., 126: (1994), 359-364], investigated the K 1,q -factorization of K m,n and gave a sufficient condition for such a factorization to exist. In papers [K 1,k -factorization of complete bipartite graphs, Discrete Math., 259: 301-306 (2002),; K p,q -factorization of complete bipartite graphs, Sci. China Ser. A-Math., 47: (2004), 473-479], Du and Wang extended Wang’s result to the case that p and q are any positive integers. In this paper, we give a sufficient condition for λK m,n to have a K p,q -factorization. As a special case, it is shown that the necessary condition for the K p,q -factorization of λK m,n is always sufficient when p : q = k : (k + 1) for any positive integer k.

Keywords: Complete bipartite multigraph; factor; factorization (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0221-z

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