### Abstract

In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface of genus g and produce a planar drawing of G in R^{2}, with a bounding face defined by a polygonal schema for P for S. Our drawings are planar, but they allow for multiple copies of vertices and edges on 's boundary, which is a common way of visualizing higher-genus graphs in the plane. As a side note, we show that it is NP-complete to determine whether a given graph embedded in a genus-g surface has a set of 2g fundamental cycles with vertex-disjoint interiors, which would be desirable from a graph-drawing perspective.

Original language | English (US) |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 45-56 |

Number of pages | 12 |

Volume | 5849 LNCS |

DOIs | |

State | Published - 2010 |

Event | 17th International Symposium on Graph Drawing, GD 2009 - Chicago, IL, United States Duration: Sep 22 2009 → Sep 25 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 5849 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 17th International Symposium on Graph Drawing, GD 2009 |
---|---|

Country | United States |

City | Chicago, IL |

Period | 9/22/09 → 9/25/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5849 LNCS, pp. 45-56). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5849 LNCS). https://doi.org/10.1007/978-3-642-11805-0_7

**Planar drawings of higher-genus graphs.** / Duncan, Christian A.; Goodrich, Michael T.; Kobourov, Stephen G.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5849 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5849 LNCS, pp. 45-56, 17th International Symposium on Graph Drawing, GD 2009, Chicago, IL, United States, 9/22/09. https://doi.org/10.1007/978-3-642-11805-0_7

}

TY - GEN

T1 - Planar drawings of higher-genus graphs

AU - Duncan, Christian A.

AU - Goodrich, Michael T.

AU - Kobourov, Stephen G

PY - 2010

Y1 - 2010

N2 - In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface of genus g and produce a planar drawing of G in R2, with a bounding face defined by a polygonal schema for P for S. Our drawings are planar, but they allow for multiple copies of vertices and edges on 's boundary, which is a common way of visualizing higher-genus graphs in the plane. As a side note, we show that it is NP-complete to determine whether a given graph embedded in a genus-g surface has a set of 2g fundamental cycles with vertex-disjoint interiors, which would be desirable from a graph-drawing perspective.

AB - In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface of genus g and produce a planar drawing of G in R2, with a bounding face defined by a polygonal schema for P for S. Our drawings are planar, but they allow for multiple copies of vertices and edges on 's boundary, which is a common way of visualizing higher-genus graphs in the plane. As a side note, we show that it is NP-complete to determine whether a given graph embedded in a genus-g surface has a set of 2g fundamental cycles with vertex-disjoint interiors, which would be desirable from a graph-drawing perspective.

UR - http://www.scopus.com/inward/record.url?scp=77951614354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951614354&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11805-0_7

DO - 10.1007/978-3-642-11805-0_7

M3 - Conference contribution

SN - 3642118046

SN - 9783642118043

VL - 5849 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 45

EP - 56

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -