Abstract

Let K m, n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A K p, q -factorization of K m, n is a set of edge-disjoint K p, q -factors of K m, n which partition the set of edges of K m, n . Martin (Discrete Math. 167/168 (1997) 461) gave simple necessary conditions for K p, q -factorization of K m, n , and conjectured these conditions are sufficient. In this paper, it is shown that Martin's conjecture on K p, q -factorization of K m, n is true for p: q=2:3.

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