### Abstract

Let a, b, m, and t be integers such that 1 ≤ a < b and 1 ≤ t ≤ [(b - m + 1)/a]. Suppose that G is a graph of order |G| and H is any subgraph of G with the size |E(H)| = m. Then we prove that G has an [a, b]-factor containing all the edges of H if the minimum degree is at least a, |G| > ((a + b)(t(a + b - 1) - 1) + 2m)/b, and |N_{G}(x_{1}) ∪... ∪N_{G}(x_{t})| ≥ (a|G| + 2m)/(a + b) for every independent set {x_{1},..., x_{t}} ⊆ V (G). This result is best possible in some sense and it is an extension of the result of H. Matsuda (A neighborhood condition for graphs to have [a, b]-factors, Discrete Mathematics 224 (2000) 289-292).

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

Pages (from-to) | 763-768 |

Number of pages | 6 |

Journal | Graphs and Combinatorics |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics

### Cite this

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

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 18, no. 4, pp. 763-768. https://doi.org/10.1007/s003730200062

}

TY - JOUR

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

AU - Matsuda, Haruhide

PY - 2002

Y1 - 2002

N2 - Let a, b, m, and t be integers such that 1 ≤ a < b and 1 ≤ t ≤ [(b - m + 1)/a]. Suppose that G is a graph of order |G| and H is any subgraph of G with the size |E(H)| = m. Then we prove that G has an [a, b]-factor containing all the edges of H if the minimum degree is at least a, |G| > ((a + b)(t(a + b - 1) - 1) + 2m)/b, and |NG(x1) ∪... ∪NG(xt)| ≥ (a|G| + 2m)/(a + b) for every independent set {x1,..., xt} ⊆ V (G). This result is best possible in some sense and it is an extension of the result of H. Matsuda (A neighborhood condition for graphs to have [a, b]-factors, Discrete Mathematics 224 (2000) 289-292).

AB - Let a, b, m, and t be integers such that 1 ≤ a < b and 1 ≤ t ≤ [(b - m + 1)/a]. Suppose that G is a graph of order |G| and H is any subgraph of G with the size |E(H)| = m. Then we prove that G has an [a, b]-factor containing all the edges of H if the minimum degree is at least a, |G| > ((a + b)(t(a + b - 1) - 1) + 2m)/b, and |NG(x1) ∪... ∪NG(xt)| ≥ (a|G| + 2m)/(a + b) for every independent set {x1,..., xt} ⊆ V (G). This result is best possible in some sense and it is an extension of the result of H. Matsuda (A neighborhood condition for graphs to have [a, b]-factors, Discrete Mathematics 224 (2000) 289-292).

UR - http://www.scopus.com/inward/record.url?scp=0036975859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036975859&partnerID=8YFLogxK

U2 - 10.1007/s003730200062

DO - 10.1007/s003730200062

M3 - Article

VL - 18

SP - 763

EP - 768

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 4

ER -