### Abstract

It is well known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n-9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded in a closed surface with Euler characteristic χ, then G contains at most 2n- min {2, 2χ} edges. This bound is best possible for every closed surface.

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

Pages (from-to) | 760 |

Number of pages | 1 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 11 |

DOIs | |

Publication status | Published - 2002 Jul |

Externally published | Yes |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

**On minimally 3-connected graphs on a surface.** / Ota, Katsuhiro.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On minimally 3-connected graphs on a surface

AU - Ota, Katsuhiro

PY - 2002/7

Y1 - 2002/7

N2 - It is well known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n-9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded in a closed surface with Euler characteristic χ, then G contains at most 2n- min {2, 2χ} edges. This bound is best possible for every closed surface.

AB - It is well known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n-9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded in a closed surface with Euler characteristic χ, then G contains at most 2n- min {2, 2χ} edges. This bound is best possible for every closed surface.

UR - http://www.scopus.com/inward/record.url?scp=34247107687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247107687&partnerID=8YFLogxK

U2 - 10.1016/S1571-0653(05)80006-X

DO - 10.1016/S1571-0653(05)80006-X

M3 - Article

AN - SCOPUS:34247107687

VL - 11

SP - 760

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -