### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Fan-type results for the existence of [ a, b ]-factors.** / Matsuda, Haruhide.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 306, no. 7, pp. 688-693. https://doi.org/10.1016/j.disc.2006.01.018

}

TY - JOUR

T1 - Fan-type results for the existence of [ a, b ]-factors

AU - Matsuda, Haruhide

PY - 2006/4/28

Y1 - 2006/4/28

N2 - 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.

AB - 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.

KW - [ a, b ]-factor

KW - Factor

KW - Fan-type

KW - Graph

KW - Neighborhood union

UR - http://www.scopus.com/inward/record.url?scp=33645851025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645851025&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2006.01.018

DO - 10.1016/j.disc.2006.01.018

M3 - Article

AN - SCOPUS:33645851025

VL - 306

SP - 688

EP - 693

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 7

ER -