### 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 |
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Pages (from-to) | 763-768 |

Number of pages | 6 |

Journal | Graphs and Combinatorics |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 Dec 1 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics