On (g, f, n)-critical graphs

Let G be a graph, and let g and f be two integer-valued functions defined on V(G) such that g(x) ≤ f(x) for all x ∈ V(G). A graph G is called a (g, f, n)-critical graph if G - N has a (g, f)-factor for each N ⊆ V(G) with |N| = 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.