Neighbor Set for the Existence of (g, f, n)-Critical Graphs

Let C be a graph of order p. Let g(x) and f (x) be two nonnegative integer-valued functions defined on V(G) with g(x) <= f (x) for any x is an element of V(C). A graph G is said to be (g, f, n)-critical if G - N has a (g, f)-factor for each N subset of V (G) with vertical bar N vertical bar = n. If g(x) a and f(x) b for all x is an element of V(G), then a (g, f,n)-critical graph is an (a,b,n)-critical graph. In this paper, several sufficient conditions in terms of neighbor set for graphs to be (a,5, n)-critical or (g, f, n)-critical are given.