### Abstract

A graph G is said to be faithfully embeddable on a closed surface F^{2} if G can be embedded on F^{2} in such a way that any automorphism of G extends to an auto-homeomorphism of F^{2}. It has been known that every 3-connected planar graph is faithfully embeddable on the sphere.We shall show that every 3-connected planar graph is faithfully embeddable on a suitable orientable closed surface other than the sphere unless it is one of seven exceptions.

Original language | English |
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Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 249-262 |

Number of pages | 14 |

Volume | 159 |

ISBN (Print) | 9783319304496 |

DOIs | |

State | Published - 2016 |

Event | 5th Workshop on Symmetries in Graphs, Maps, and Polytopes, SIGMAP 2014 - Malvern, United Kingdom |

### Other

Other | 5th Workshop on Symmetries in Graphs, Maps, and Polytopes, SIGMAP 2014 |
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Country | United Kingdom |

City | Malvern |

Period | 14/7/7 → 14/7/11 |

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Springer Proceedings in Mathematics and Statistics.*(Vol. 159, pp. 249-262). Springer New York LLC. DOI: 10.1007/978-3-319-30451-9_12

**Faithful embeddings of planar graphs on orientable closed surfaces.** / Negami, Seiya.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Springer Proceedings in Mathematics and Statistics.*vol. 159, Springer New York LLC, pp. 249-262, 5th Workshop on Symmetries in Graphs, Maps, and Polytopes, SIGMAP 2014, Malvern, United Kingdom, 7-11 July. DOI: 10.1007/978-3-319-30451-9_12

}

TY - CHAP

T1 - Faithful embeddings of planar graphs on orientable closed surfaces

AU - Negami,Seiya

PY - 2016

Y1 - 2016

N2 - A graph G is said to be faithfully embeddable on a closed surface F2 if G can be embedded on F2 in such a way that any automorphism of G extends to an auto-homeomorphism of F2. It has been known that every 3-connected planar graph is faithfully embeddable on the sphere.We shall show that every 3-connected planar graph is faithfully embeddable on a suitable orientable closed surface other than the sphere unless it is one of seven exceptions.

AB - A graph G is said to be faithfully embeddable on a closed surface F2 if G can be embedded on F2 in such a way that any automorphism of G extends to an auto-homeomorphism of F2. It has been known that every 3-connected planar graph is faithfully embeddable on the sphere.We shall show that every 3-connected planar graph is faithfully embeddable on a suitable orientable closed surface other than the sphere unless it is one of seven exceptions.

UR - http://www.scopus.com/inward/record.url?scp=84962704307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962704307&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-30451-9_12

DO - 10.1007/978-3-319-30451-9_12

M3 - Conference contribution

SN - 9783319304496

VL - 159

SP - 249

EP - 262

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -