  The $d$-dimensional hypercube graph $Q_d$ has as vertices all subsets of
$\{1,\ldots,d\}$, and an edge between any two sets that differ in a single
element. The Ruskey-Savage conjecture asserts that every matching of $Q_d$,
$d\ge 2$, can be extended to a Hamilton cycle, i.e., to a cycle that visits
every vertex exactly once. We prove that every matching of $Q_d$, $d\ge 2$, can
be extended to a cycle that visits at least a $2/3$-fraction of all vertices.
