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

Let G 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∈V(G). A graph G is said to be (g,f,n)-critical if G−N has a (g,f)-factor for each N⊆V(G) with |N|=n. If g(x)≡a and f(x)≡b for all x∈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; b; n)-critical or (g,f,n)-critical are given.