### Abstract

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

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

Pages | 83-94 |

Number of pages | 12 |

Volume | 8242 LNCS |

DOIs | |

State | Published - 2013 |

Event | 21st International Symposium on Graph Drawing, GD 2013 - Bordeaux, France Duration: Sep 23 2013 → Sep 25 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8242 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 21st International Symposium on Graph Drawing, GD 2013 |
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Country | France |

City | Bordeaux |

Period | 9/23/13 → 9/25/13 |

### 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. 8242 LNCS, pp. 83-94). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8242 LNCS). https://doi.org/10.1007/978-3-319-03841-4-8

**Straight-line grid drawings of 3-connected 1-planar graphs.** / Alam, Md Jawaherul; Brandenburg, Franz J.; 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. 8242 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8242 LNCS, pp. 83-94, 21st International Symposium on Graph Drawing, GD 2013, Bordeaux, France, 9/23/13. https://doi.org/10.1007/978-3-319-03841-4-8

}

TY - GEN

T1 - Straight-line grid drawings of 3-connected 1-planar graphs

AU - Alam, Md Jawaherul

AU - Brandenburg, Franz J.

AU - Kobourov, Stephen G

PY - 2013

Y1 - 2013

N2 - A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

AB - A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

UR - http://www.scopus.com/inward/record.url?scp=84891887533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891887533&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-03841-4-8

DO - 10.1007/978-3-319-03841-4-8

M3 - Conference contribution

AN - SCOPUS:84891887533

SN - 9783319038407

VL - 8242 LNCS

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

SP - 83

EP - 94

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

ER -