On $r$-extendability of the hypercube $Q\sb n$
Nirmala B. Limaye, Dinesh G. Sarvate · Mathematica Bohemica · 1997
A graph having a perfect matching is called $r$-extendable if every matching of size $r$ can be extended to a perfect matching. It is proved that in the hypercube $Q_n$, a matching $S$ with $ |S|\leq n$ can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, $Q_n$ is $r$-extendable for every $r$ with $1\leq r\leq n-1.$