On toughness and fractional (g,f,n)-critical graphs

Let G be a graph with vertex set V(G). For any S⊆V(G) we use ω(G−S) to denote the number of components of G−S. The toughness of G, t(G), is defined as if G is not complete; otherwise, set t(G)=+∞. In this paper, we consider the relationship between the toughness and fractional (g,f,n)-critical graphs. It is proved that a graph G is a (g,f,n)-critical graph if t(G)⩾(b2−1)(n+1)/a.