On Toughness and Fractional \(f\)-Factors

Abstract

In this paper, we consider the relationship between the toughness and the existence of fractional \(f\)-factors. It is proved that a graph $G$ has a fractional \(f\)-factor if \(t(G) \geq \frac{b^2+b}{a}-\frac{b+1}{b}\). Furthermore, we show that the result is best possible in some sense.