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

Abstract

Let G = (V, E) be a k-connected graph. For t >= 3 a subset T subset of V is a (t, k)-shredder if vertical bar T vertical bar = 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.