Orthogonal factorization for two bipartite digraphs in computer networks

Many real-world networks problems modeled by digraphs. In this paper, we study orthogonal factorization for two classes of bipartite digraph, and give following results: 1) Let G be a bipartite (mg+1, mf)-digraph．M is a subdigraph of G with m arcs and M is also a match, then for any fix arc e in M, there is a (g,f)-factor F such that F contain e and not contain other m?1 arcs in M; 2) Let G be a bipartite (mg, mf?1)-digraph. It is proved that if g(x)?1, H is a subdigraph of G with m arcs, then G has a (g, f)-factorization orthogonal to H ; or if g(x) ? 2, H is a subdigraph of G with 2m arcs, then G has a (g, f) -factorization 2-orthogonal to H.