### 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 |
---|---|

Pages (from-to) | 319-324 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 259 |

Issue number | 1-3 |

Publication status | Published - 2002 Dec 28 |

### Keywords

- 1-Factors
- Closures
- Factor-critical graphs

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*259*(1-3), 319-324.

**A closure concept in factor-critical graphs.** / Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 259, no. 1-3, pp. 319-324.

}

TY - JOUR

T1 - A closure concept in factor-critical graphs

AU - Nishimura, Tsuyoshi

PY - 2002/12/28

Y1 - 2002/12/28

N2 - 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 ∈ NG(u) ∩ NG(v), and NG(x) ⊂ NG(u) ∪ NG(v) ∪ {u,v}. Then G is n-factor-critical if and only if G + uv is n-factor-critical.

AB - 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 ∈ NG(u) ∩ NG(v), and NG(x) ⊂ NG(u) ∪ NG(v) ∪ {u,v}. Then G is n-factor-critical if and only if G + uv is n-factor-critical.

KW - 1-Factors

KW - Closures

KW - Factor-critical graphs

UR - http://www.scopus.com/inward/record.url?scp=33845790755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845790755&partnerID=8YFLogxK

M3 - Article

VL - 259

SP - 319

EP - 324

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -