On (t, k)-shredders in k-connected graphs

Let G = (V, E) be a k-connected graph. For t ≥ 3 a subset T ⊂ V is a (t, k)-shredder if |T| = k and G - T has at least t connected components. It is known that the number of (t, k)-shredders in a k-connected graph on n nodes is less than 2n /(2t - 3). We show a slightly better bound for the case k ≤ 2t - 3.