[0,k_i]₁^m-Factorizations Orthogonal to a Subgraph

Let G be a graph,k₁,…,k_m be positive integers.If the edges of graph G can be decom- posed into some edge disjoint [0,k₁]-factor F₁…,[0,k_m]-factor F_m then we can say F={F₁,…,F_m},is a [0,k_i]₁^m-factorization of G.If H is a subgraph with m edges in graph G and |E(H)∩E(F_i)|=1 for all 1≤i≤m,then we can call that F is orthogonal to H.It is proved that if G is a[0,k₁+… +k_m-m+1]-graph,H is a subgraph with m edges in G,then graph G has a [0,k_i]₁^m-factorization orthogonal to H.