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On r -extendability of the hypercube Q n

Nirmala B. LimayeDinesh 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 | 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 r n - 1 .

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