  We say that a graph G is $(k,\ell)$-stable if removing $k$ vertices from it
reduces its independence number by at most $\ell$. We say that G is tight
$(k,\ell)$-stable if it is $(k,\ell)$-stable and its independence number equals
$\lfloor{\frac{n-k+1}{2}\rfloor}+\ell$, the maximum possible, where $n$ is the
vertex number of G. Answering a question of Dong and Wu, we show that every
tight $(2,0)$-stable graph with odd vertex number must be an odd cycle.
Moreover, we show that for all $k\geq 3$, every tight $(k,0)$-stable graph has
at most $k+6$ vertices.
