A binding number condition for graphs to be (a, b, k)-critical graphs

Let a and b be two even integers with 2 ⩽ a < b, and let k be a nonnegative integer. Let G be a graph of order n. Its binding number bind(G) is defined as follows,bind(G)=min|NG(X)||X|:∅≠X⊆V(G),NG(X)≠V(G).In this paper, it is proved that G is an (a, b, k  )-critical graph if bind(G)>(a+b-1)(n-1)bn-(a+b)-bk+3 and n⩾(a+b)(a+b-3)b+bkb-1. Furthermore, it is shown that the result in this paper is best possible in some sense.