Abstract
A connected graph of order at least 2k+2 is k-extendable for a non-negative integer k if it contains a perfect matching and every matching of size k can be extended to a perfect matching. The extendability number of the graph is the maximum k such that the graph is k-extendable. In this paper, we prove that, for a Cayley graph Γ of a symmetric group with respect to a generating set of size m consisting of transpositions, the extendability number of Γ is m−1.
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