Toughness and \([a, b]\)-factors in Graphs

Abstract

In this paper, we consider the relationship between toughness and the existence of \([a, b]\)-factors. We obtain that a graph \(G\) has an \([a, b]\)-factor if \(t(G) \geq {a-1} + \frac{a-1}{b}\) with \(b > a > 1\). Furthermore, it is shown that the result is best possible in some sense.