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