A Note on Near-factor-critical Graphs
Combinatorics
2014-05-19 v2
Abstract
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.
Cite
@article{arxiv.1404.5416,
title = {A Note on Near-factor-critical Graphs},
author = {Kuo-Ching Huang and Ko-Wei Lih},
journal= {arXiv preprint arXiv:1404.5416},
year = {2014}
}
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4 pages