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arXiv · 1404.5416

A Note on Near-factor-critical Graphs

Kuo-Ching Huang·Ko-Wei Lih
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Abstract

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

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Kuo-Ching Huang, Ko-Wei Lih. 2014-05-16. A Note on Near-factor-critical Graphs. https://arxiv.org/abs/1404.5416

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