### 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 |

### Fingerprint

### Keywords

- Mathemacics Subject Classification (1991): 05C40

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

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

**Non-contractible edges in a 3-connected graph.** / Egawa, Yoshimi; Ota, Katsuhiro; Saito, Akira; Yu, Xingxing.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 15, no. 3, pp. 357-364. https://doi.org/10.1007/BF01299741

}

TY - JOUR

T1 - Non-contractible edges in a 3-connected graph

AU - Egawa, Yoshimi

AU - Ota, Katsuhiro

AU - Saito, Akira

AU - Yu, Xingxing

PY - 1995/9

Y1 - 1995/9

N2 - 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.

AB - 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.

KW - Mathemacics Subject Classification (1991): 05C40

UR - http://www.scopus.com/inward/record.url?scp=0012960835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012960835&partnerID=8YFLogxK

U2 - 10.1007/BF01299741

DO - 10.1007/BF01299741

M3 - Article

AN - SCOPUS:0012960835

VL - 15

SP - 357

EP - 364

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 3

ER -