A graph G having a 1-factor is called n-extendible if every matching of size n extends to a 1-factor. Let G be a 2-connected graph of order 2p. Let r ≥ 0 and n > 0 be integers such that p - r ≥ n + 1. It is shown that if G\S is n-extendible for every connected subgraph S of order 2r for which G\S is connected, then G is n-extendible.
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