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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