  Let $L(G)$ denote the maximum number of leaves in any spanning tree of a
connected graph $G$. We show the (known) result that for the $n$-cube $Q_n$,
$L(Q_n) \sim 2^n = |V(Q_n)|$ as $n\rightarrow \infty$. Examining this more
carefully, consider the minimum size of a connected dominating set of vertices
$\gamma_c(Q_n)$, which is $2^n-L(Q_n)$ for $n\ge2$. We show that
$\gamma_c(Q_n)\sim 2^n/n$. We use Hamming codes and an "expansion" method to
construct leafy spanning trees in $Q_n$.
