### Abstract

We study conditions for a simple graph G or its complement Ḡ to have a 1-factor. Let G be a graph of even order n and denote by ir(G) the difference between the maximum degree and the minimum degree of G. We prove that if both G and Ḡ are connected and ir(G) ≤ [1/4n + 1], then either G or Ḡ has a 1-factor with the inequality being sharp.

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

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 203 |

Issue number | 1-3 |

Publication status | Published - 1999 May 28 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*203*(1-3), 1-8.

**A degree condition for the existence of 1-factors in graphs or their complements.** / Ando, Kiyoshi; Kaneko, Atsushi; Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 203, no. 1-3, pp. 1-8.

}

TY - JOUR

T1 - A degree condition for the existence of 1-factors in graphs or their complements

AU - Ando, Kiyoshi

AU - Kaneko, Atsushi

AU - Nishimura, Tsuyoshi

PY - 1999/5/28

Y1 - 1999/5/28

N2 - We study conditions for a simple graph G or its complement Ḡ to have a 1-factor. Let G be a graph of even order n and denote by ir(G) the difference between the maximum degree and the minimum degree of G. We prove that if both G and Ḡ are connected and ir(G) ≤ [1/4n + 1], then either G or Ḡ has a 1-factor with the inequality being sharp.

AB - We study conditions for a simple graph G or its complement Ḡ to have a 1-factor. Let G be a graph of even order n and denote by ir(G) the difference between the maximum degree and the minimum degree of G. We prove that if both G and Ḡ are connected and ir(G) ≤ [1/4n + 1], then either G or Ḡ has a 1-factor with the inequality being sharp.

UR - http://www.scopus.com/inward/record.url?scp=0345884754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345884754&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0345884754

VL - 203

SP - 1

EP - 8

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -