### Abstract

An edge e in a 3-connected graph G is contractible if the contraction of e in G results in a 3-connected graph; otherwise e is non-contractible. In this paper, we prove that the number of non-contractible edges in a 3-connected graph of order p≥5 is at most {Mathematical expression} and show that this upper bound is the best possible for infinitely many values of p.

Original language | English |
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Pages (from-to) | 357-364 |

Number of pages | 8 |

Journal | Combinatorica |

Volume | 15 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1995 Sep 1 |

### Keywords

- Mathemacics Subject Classification (1991): 05C40

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

Egawa, Y., Ota, K., Saito, A., & Yu, X. (1995). Non-contractible edges in a 3-connected graph.

*Combinatorica*,*15*(3), 357-364. https://doi.org/10.1007/BF01299741