It is known that if $n$ vertices can be removed from a connected graph $Γ$ so that no subgraphs isomorphic to the graph $K$ remain, then no more than $|V(K)|\cdot n$ vertices can be removed, forming a set invariant with respect to all automorphisms of the graph $Γ$, so that no subgraphs isomorphic to the graph $K$ remain. We construct an infinite set of (connected) graphs $K$ for which this estimate is not exact.
