Randomly r-orthogonal factorizations in bipartite graphs

Let G be a graph with vertex set V(G) and edge set E(G), and let f be an integer-valued function defined on V(G). It is proved in this paper that every bipartite (0,mf-m+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0,mf-m+1)$$\end{document}-graph has a (0, f)-factorization randomly r-orthogonal to n vertex-disjoint mr-subgraphs of G, which is a generalization of the known result with n=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1$$\end{document} given by Zhou and Wu.