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On $r$ -extendability of the hypercube $Q_{n}$

Nirmala B. Limaye; Dinesh G. Sarvate — 1997

Mathematica Bohemica

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 $1 \leq r \leq n - 1 .$

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On r -extendability of the hypercube Q n

On $r$ -extendability of the hypercube $Q_{n}$