### Abstract

Let a, b, k, and m be positive integers such that 1 ≤a < b and 2 k (b + 1 - m)/a. Let G = (V(G), E(G)) be a graph of order |G|. Suppose that |G| > (a + b)(k(a + b - 1) - 1)/b and |N _{G} (x _{1}) ∪ N _{G} (x _{2})... ∪ N _{G} (x_{k} )| ≥ a|G|/(a + b) for every independent set { x _{1}, x _{2}, ..., x _{k}} ⊆ V(G). Then for any subgraph H of G with m edges and δ(G - E(H))≥ a, G has an [a, b]-factor F such that E(H)∩ E(F) = θ. This result is best possible in some sense and it is an extension of the result of Matsuda (Discrete Mathematics 224 (2000) 289-292).

Original language | English |
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Title of host publication | Discrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers |

Pages | 70-78 |

Number of pages | 9 |

DOIs | |

Publication status | Published - 2007 Dec 1 |

Event | 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an, China Duration: 2005 Nov 22 → 2005 Nov 24 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4381 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 |
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Country | China |

City | Xi'an |

Period | 05/11/22 → 05/11/24 |

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Kano, M., & Matsuda, H. (2007). A Neighborhood Condition for Graphs to Have [a, b]-Factors III. In

*Discrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers*(pp. 70-78). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4381 LNCS). https://doi.org/10.1007/978-3-540-70666-3_8