### Abstract

Let 1 ≤ a < b be integers and G a graph of order n sufficiently large for a and b. Then G has an [ a, b ]-factor if the minimum degree is at least a and every pair of vertices distance two apart has cardinality of the neighborhood union at least an / ( a + b ). This lower bound is sharp. As a consequence, we have a Fan-type condition for a graph to have an [ a, b ]-factor.

Original language | English |
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Pages (from-to) | 688-693 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 306 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2006 Apr 28 |

Externally published | Yes |

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### Keywords

- [ a, b ]-factor
- Factor
- Fan-type
- Graph
- Neighborhood union

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science