A Note on Near-factor-critical Graphs


A near-factor of a finite simple graph GG is a matching that saturates all vertices except one. A graph GG is said to be near-factor-critical if the deletion of any vertex from GG results in a subgraph that has a near-factor. We prove that a connected graph GG is near-factor-critical if and only if it has a perfect matching. We also characterize disconnected near-factor-critical graphs.Comment: 4 page

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