On -extendability of the hypercube
Nirmala B. Limaye, Dinesh G. Sarvate (1997)
Mathematica Bohemica
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A graph having a perfect matching is called -extendable if every matching of size can be extended to a perfect matching. It is proved that in the hypercube , a matching with can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, is -extendable for every with