### Abstract

A graph G is called n-factor-critical if the removal of every set of n vertices results in a graph with a 1-factor. We prove the following theorem: Let G be a graph and let x be a locally n-connected vertex. Let {μ, v} be a pair of vertices in V(G) - {x} such that uv E(G), x ∈ N_{G}(u) ∩ N_{G}(v), and N_{G}(x) ⊂ N_{G}(u) ∪ N_{G}(v) ∪ {u,v}. Then G is n-factor-critical if and only if G + uv is n-factor-critical.

Original language | English |
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Pages (from-to) | 319-324 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 259 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2002 Dec 28 |

### Keywords

- 1-Factors
- Closures
- Factor-critical graphs

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Nishimura, T. (2002). A closure concept in factor-critical graphs.

*Discrete Mathematics*,*259*(1-3), 319-324. https://doi.org/10.1016/S0012-365X(02)00303-5