9-Shredders in 9-connected graphs

Abstract

For a graph $G$, a subset $S$ of $V(G)$ is called a shredder if $G-S$ consists of three or more components. We show that if $G$ is a 9-connected graph of order at least 67, then the number of shredders of cardinality 9 of $G$ is less than or equal to $(2|V(G)|-9)/3$.