### Abstract

Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.

Original language | English |
---|---|

Pages (from-to) | 2382-2388 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2008 Jun 28 |

Externally published | Yes |

### Fingerprint

### Keywords

- Degree sum
- Linear forest
- Long cycle

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*308*(12), 2382-2388. https://doi.org/10.1016/j.disc.2007.05.005

**A degree sum condition for long cycles passing through a linear forest.** / Fujisawa, Jun; Yamashita, Tomoki.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 308, no. 12, pp. 2382-2388. https://doi.org/10.1016/j.disc.2007.05.005

}

TY - JOUR

T1 - A degree sum condition for long cycles passing through a linear forest

AU - Fujisawa, Jun

AU - Yamashita, Tomoki

PY - 2008/6/28

Y1 - 2008/6/28

N2 - Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.

AB - Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.

KW - Degree sum

KW - Linear forest

KW - Long cycle

UR - http://www.scopus.com/inward/record.url?scp=41549131212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41549131212&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2007.05.005

DO - 10.1016/j.disc.2007.05.005

M3 - Article

VL - 308

SP - 2382

EP - 2388

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

ER -