(C)over-capk-factorization of symmetric complete bipartite and tripartite multi-digraphs

We show that a necessary and sufficient condition for the existence of a (C) over cap(k)-factorization of the symmetric complete bipartite multi-digraph lambda K-n1,K-n2* is (i) k = 0 (mod 2) and (ii) n(1) = n(2) = 0 (modk/2). We also show that a necessary and sufficient condition for the existence of a (C) over cap(k)-factorization of the symmetric complete tripartite multi-digraph lambda K-n1,K-n2n3 is (i) k = 0 (mod 2) and (ii) n(1) = n(2) = n(3) = 0 (mod k). (C) 2000 Elsevier Science B.V. All rights reserved.