### Abstract

An edge e of a 3‐connected graph G is said to be removable if G ‐ e is a subdivision of a 3‐connected graph. If e is not removable, then e is said to be nonremovable. In this paper, we study the distribution of removable edges in 3‐connected graphs and prove that a 3‐connected graph of order n ≥ 5 has at most [(4 n — 5)/3] nonremovable edges.

Original language | English |
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Pages (from-to) | 465-473 |

Number of pages | 9 |

Journal | Journal of Graph Theory |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1990 |

Externally published | Yes |

### Cite this

*Journal of Graph Theory*,

*14*(4), 465-473. https://doi.org/10.1002/jgt.3190140410

}

*Journal of Graph Theory*, vol. 14, no. 4, pp. 465-473. https://doi.org/10.1002/jgt.3190140410

**Removable edges in 3‐connected graphs.** / Holton, Derek A.; Jackson, Bill; Saito, Akira; Wormald, Nicholas C.

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

TY - JOUR

T1 - Removable edges in 3‐connected graphs

AU - Holton, Derek A.

AU - Jackson, Bill

AU - Saito, Akira

AU - Wormald, Nicholas C.

PY - 1990

Y1 - 1990

N2 - An edge e of a 3‐connected graph G is said to be removable if G ‐ e is a subdivision of a 3‐connected graph. If e is not removable, then e is said to be nonremovable. In this paper, we study the distribution of removable edges in 3‐connected graphs and prove that a 3‐connected graph of order n ≥ 5 has at most [(4 n — 5)/3] nonremovable edges.

AB - An edge e of a 3‐connected graph G is said to be removable if G ‐ e is a subdivision of a 3‐connected graph. If e is not removable, then e is said to be nonremovable. In this paper, we study the distribution of removable edges in 3‐connected graphs and prove that a 3‐connected graph of order n ≥ 5 has at most [(4 n — 5)/3] nonremovable edges.

UR - http://www.scopus.com/inward/record.url?scp=84986439477&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190140410

DO - 10.1002/jgt.3190140410

M3 - Article

VL - 14

SP - 465

EP - 473

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 4

ER -