### Abstract

We prove the following: (1) Let G be a graph with a 1-factor and let F be an arbitrary 1-factor of G. If G \ {a,b} is k-extendable for each ab ∈ F, then G is k-extendable. (2) Let G be a graph and let M be an arbitrary maximal matching of G. If G \ {a, b} is k-factor-critical for each ab ∈ M, then G is k-factor-critical.

Original language | English |
---|---|

Pages (from-to) | 285-290 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 222 |

Issue number | 1-3 |

Publication status | Published - 2000 Jul 28 |

### Keywords

- 1-factor
- k-extendable
- k-factor-critical
- Matching

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**On 1-factors and matching extension.** / Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 222, no. 1-3, pp. 285-290.

}

TY - JOUR

T1 - On 1-factors and matching extension

AU - Nishimura, Tsuyoshi

PY - 2000/7/28

Y1 - 2000/7/28

N2 - We prove the following: (1) Let G be a graph with a 1-factor and let F be an arbitrary 1-factor of G. If G \ {a,b} is k-extendable for each ab ∈ F, then G is k-extendable. (2) Let G be a graph and let M be an arbitrary maximal matching of G. If G \ {a, b} is k-factor-critical for each ab ∈ M, then G is k-factor-critical.

AB - We prove the following: (1) Let G be a graph with a 1-factor and let F be an arbitrary 1-factor of G. If G \ {a,b} is k-extendable for each ab ∈ F, then G is k-extendable. (2) Let G be a graph and let M be an arbitrary maximal matching of G. If G \ {a, b} is k-factor-critical for each ab ∈ M, then G is k-factor-critical.

KW - 1-factor

KW - k-extendable

KW - k-factor-critical

KW - Matching

UR - http://www.scopus.com/inward/record.url?scp=0347646890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347646890&partnerID=8YFLogxK

M3 - Article

VL - 222

SP - 285

EP - 290

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -