  For any graph $G$, let $\iota_{\rm c}(G)$ denote the size of a smallest set
$D$ of vertices of $G$ such that the graph obtained from $G$ by deleting the
closed neighbourhood of $D$ contains no cycle. We prove that if $G$ is a
connected $n$-vertex graph that is not a triangle, then $\iota_{\rm c}(G) \leq
n/4$. We also show that the bound is sharp. Consequently, we solve a problem of
Caro and Hansberg.
