(g, f)-factorizations orthogonal to a star in graphs

Let G be a graph, and F={F1, F2,…,Fm} and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with Fi for all i, 1≤i≤m, then we say that F is orthogonal to H. Let g and f be two integer-valued functions defined on V(G) such that 0≤g(x)≤f(x) for every x∈V(G). In this paper, it is proved that for any given star with m edges of an (mg+m-1, mf-m + 1)-graph G, there exists a (g,f)-factorization of G orthogonal to it.