Subdigraphs with orthogonal factorizations of digraphs

Let G = (V, E) be a digraph and let g and f be two pairs of integervalued functions defined on V such that n <= g(x) < f (x) for every x is an element of V. Let H-1, H-2,., H-n, be arc-disjoint k-subdigraphs of G. In this article, we prove that every (mg + k - 1, mf - k + 1)-digraph G contains a subdigraph R such that R has a (g,f)-factorization orthogonal to H, (1 <= i <= n), where m and k are positive integers with 1 <= k <= m. (C) 2012 Elsevier Ltd. All rights reserved.