(t,k)-Shredders in k-Connected Graphs

Abstract

Let t, k be integers with t≥3 and k≥1. For a graph G, a subset S of V(G) with cardinality k is called a (t,k)-shredder if G−S consists of t or more components. In this paper, we show that if t≥3, 2(t−1)≤k≤3t−5 and G is a k-connected graph of order at least k8, then the number of (t,k)-shredders of G is less than or equal to ((2t−1)(|V(G)|−f(|V(G)|)))/(2(t−1)2), where f(n) denotes the unique real number x with x≥k−1 such that n=2(t−1)2(kx)+x.