English

A Note on Near-factor-critical Graphs

Combinatorics 2014-05-19 v2

Abstract

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.

Keywords

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}
}

Comments

4 pages

R2 v1 2026-06-22T03:55:28.532Z