  Let $G$ be a graph on $V$. A vertex subset $S \subset V$ is called a cover of
$G$ if its complement is an independent set, and $S$ is called a noncover if it
is not a cover of $G$. A noncover complex $NC(G)$ of $G$ is the simplicial
complex on $V$ whose faces are noncovers of $G$. The independence domination
number $ i\gamma(G)$ of $G$ is the minimum integer $k$ such that every
independent set of $G$ can be dominated by $k$ vertices. In this note, we prove
that $NC(G)$ is $(|V|- i\gamma(G)-1)$-collapsible.
