### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 743-753 |

Number of pages | 11 |

Journal | Graphs and combinatorics |

Volume | 30 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- MSC-05C38
- MSC-05C40
- MSC-05C75
- EWI-24777
- IR-91192
- Chord
- 3-Connected graph
- METIS-304108
- Removable edge

### Cite this

*Graphs and combinatorics*,

*30*(3), 743-753. https://doi.org/10.1007/s00373-013-1296-x

}

*Graphs and combinatorics*, vol. 30, no. 3, pp. 743-753. https://doi.org/10.1007/s00373-013-1296-x

**Removable edges and chords of longest cycles in 3-connected graphs.** / Wu, J.; Broersma, Haitze J.; Kang, Haiyan.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Removable edges and chords of longest cycles in 3-connected graphs

AU - Wu, J.

AU - Broersma, Haitze J.

AU - Kang, Haiyan

N1 - eemcs-eprint-24777

PY - 2014

Y1 - 2014

N2 - We verify two special cases of Thomassen’s conjecture of 1976 stating that every longest cycle in a 3-connected graph contains a chord. We prove that Thomassen’s conjecture is true for two classes of 3-connected graphs that have a bounded number of removable edges on or off a longest cycle. Here an edge e of a 3-connected graph G is said to be removable if G-e is still 3-connected or a subdivision of a 3-connected (multi)graph. We give examples to show that these classes are not covered by previous results.

AB - We verify two special cases of Thomassen’s conjecture of 1976 stating that every longest cycle in a 3-connected graph contains a chord. We prove that Thomassen’s conjecture is true for two classes of 3-connected graphs that have a bounded number of removable edges on or off a longest cycle. Here an edge e of a 3-connected graph G is said to be removable if G-e is still 3-connected or a subdivision of a 3-connected (multi)graph. We give examples to show that these classes are not covered by previous results.

KW - MSC-05C38

KW - MSC-05C40

KW - MSC-05C75

KW - EWI-24777

KW - IR-91192

KW - Chord

KW - 3-Connected graph

KW - METIS-304108

KW - Removable edge

U2 - 10.1007/s00373-013-1296-x

DO - 10.1007/s00373-013-1296-x

M3 - Article

VL - 30

SP - 743

EP - 753

JO - Graphs and combinatorics

JF - Graphs and combinatorics

SN - 0911-0119

IS - 3

ER -