(g,f)-Factorization with constraints in bipartite graphs

Let G=(X,Y,E) be a bipartite graph and let g and f be two positive integer functions defined on V(G) with g(x)f(x) for each x∈V(G).Let G is(mg,mf-1)-graph.It is proved that ①if g(x)≥1,H is a subgraph of G with m edges,then G has a(g,f)-factorization orthogonal to H;②if g(x)≥2,H is a subgraph of G with 2m edges,then G has a(g,f)-factorization 2-orthogonal to H.