  Given a graph $G$, the non-cover complex of $G$ is the combinatorial
Alexander dual of the independence complex of $G$. Aharoni asked if the
non-cover complex of a graph $G$ without isolated vertices is $(|V(G)|-i
\gamma(G)-1)$-collapsible where $i \gamma(G)$ denotes the independent
domination number of $G$. Extending a result by the second author, who verified
Aharoni's question in the affirmative for chordal graphs, we prove that the
answer to the question is yes for all graphs. Namely, we show that for a graph
$G$, the non-cover complex of a graph $G$ is $(|V(G)|-i
\gamma(G)-1)$-collapsible.
