P→5-factorization of symmetric complete bipartite multi-digraphs

Abstract

It is shown that a necessary and sufficient condition for the existence of a P^→₅-factorization of symmetric complete bipartite multi-digraph λK_m,n* is (1) 3n ≥ 2m, (2) 3m ≥ 2n, (3) m + n ≡ 0 (mod 5), and (4) 5λmn/[2(m + n)] is an integer.