Let \(G\) be a graph of order \(n\), and let \(a, b, k\) be nonnegative integers with \(1 \leq a \leq b\). A spanning subgraph \(F\) of \(G\) is called an \([a, b]\)-factor if \(a \leq d_F(x) \leq b\) for each \(x \in V(G)\). Then a graph \(G\) is called an \((a, b, k)\)-critical graph if \(G – N\) has an \([a, b]\)-factor for each \(N \subseteq V(G)\) with \(|N| = k\). In this paper, it is proved that \(G\) is an \((a, b, k)\)-critical graph if \(n \geq \frac{(a+b-1)(a+b-2)}{b} +\frac{bk}{b-1}\), \(bind(G) \geq \frac{(a+b-1)(n-1)}{b(n-1-k)}\), and \(\delta(G) \neq \left\lfloor \frac{(a-1)n+a+b+bk-2}{a+b-1} \right\rfloor\).