Connected Factors in K1,n-free Graphs Containing a (g, f)-factor

Let G be a connected K1,n-free graph (n≥3), f and g be positive integer-valued functions defined on V(G) with g(v)≤f(v) for all v∈V(G). We prove that G contains a connected (g,f+n−1)-factor if G has a (g,f)-factor. This result is sharp from the point of view that there exists a connected K1,n-free graph which has a (g,f)-factor but no connected (g,f+n−2)-factor for all pairs of positive integer-valued functions g and f with g=f.