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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 Qₙ, a matching S with |S| n can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, Qₙ is r-extendable for every r with 1 r n-1.
Limaye et al. (Wed,) studied this question.