The existence of subdigraphs with orthogonal factorizations in digraphs

Let G be a [0, k(1) + k(2) + ... + k(m) - n + 1]-digraph and H-1, H-2, ..., H-r be r vertex-disjoint n-subdigraphs of G, where m, n, r and k(i) (1 <= i <= m) are positive integers satisfying 1 <= n <= m and k(1) >= k(2) >= ... k(m) >= r + 1. In this article, we verify that there exists a subdigraph R of G such that R possesses a [0, k(i)](1)(n) -factorization orthogonal to every H-i for 1 <= i <= r.