### 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 | Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers |

Pages | 83-94 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 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) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Alam, M. J., Brandenburg, F. J., & Kobourov, S. G. (2013). Straight-line grid drawings of 3-connected 1-planar graphs. In

*Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers*(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