On the number of shredders
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A subset $S$ of $k$ vertices in a $k$-connected graph $G$ is a shredder if $G-S$ has at least three components. We show that if $G$ has $n$ vertices then the number of shredders is at most $n$, which was conjectured by Cheriyan and Thurimella. If $G$ contains no meshing shredders (in particular if $k\leq 3$), the sharp upper bound $\lfloor (n-k-1)/2 \rfloor$ is proven.
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