### Abstract

Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |N_{G}(X) ∪ N_{G}(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

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

Pages (from-to) | 289-292 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 224 |

Issue number | 1-3 |

Publication status | Published - 2000 Sep 28 |

Externally published | Yes |

### Fingerprint

### Keywords

- [a, b]-factor
- Factor
- Graph
- Neighborhood

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*224*(1-3), 289-292.

**A neighborhood condition for graphs to have [a, b]-factors.** / Matsuda, Haruhide.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 224, no. 1-3, pp. 289-292.

}

TY - JOUR

T1 - A neighborhood condition for graphs to have [a, b]-factors

AU - Matsuda, Haruhide

PY - 2000/9/28

Y1 - 2000/9/28

N2 - Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

AB - Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

KW - [a, b]-factor

KW - Factor

KW - Graph

KW - Neighborhood

UR - http://www.scopus.com/inward/record.url?scp=0002733531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002733531&partnerID=8YFLogxK

M3 - Article

VL - 224

SP - 289

EP - 292

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -