On (g, f, n)-critical graphs

Let G be a. graph, and let 9 and f be two integer-valued functions defined on V(G) such that, g(x) <= f(x) for all x is an element of V(G). A graph G is called a (g, f,n)-critical graph if G - N has a (q, f)-factor for each N C V(G) with vertical bar N vertical bar = n. In this paper, a necessary and sufficient condition for a graph to be (g, f, n)-critical is given. Furthermore, the properties of (g, f, n)-critical graph are studied.