### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 70-78 |

Number of pages | 9 |

Volume | 4381 LNCS |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

Event | 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

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

City | Xi'an |

Period | 05/11/22 → 05/11/24 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4381 LNCS, 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

**A Neighborhood Condition for Graphs to Have [a, b]-Factors III.** / Kano, M.; Matsuda, Haruhide.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 4381 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4381 LNCS, pp. 70-78, 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, Xi'an, 05/11/22. https://doi.org/10.1007/978-3-540-70666-3_8

}

TY - GEN

T1 - A Neighborhood Condition for Graphs to Have [a, b]-Factors III

AU - Kano, M.

AU - Matsuda, Haruhide

PY - 2007

Y1 - 2007

N2 - 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 (xk )| ≥ 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).

AB - 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 (xk )| ≥ 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).

KW - [a, b]-factor

KW - Factor

KW - Neighborhood union

UR - http://www.scopus.com/inward/record.url?scp=49949116358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49949116358&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-70666-3_8

DO - 10.1007/978-3-540-70666-3_8

M3 - Conference contribution

AN - SCOPUS:49949116358

SN - 3540706658

SN - 9783540706656

VL - 4381 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 70

EP - 78

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -