### Abstract

Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual on a small integer grid such that the edges are drawn as straight-line segments and the only crossings are between primal-dual pairs of edges. We provide an O(n) time algorithm that simultaneously embeds a 3-connected planar graph and its dual on a (2n - 2) × (2n - 2) integer grid, where n is the total number of vertices in the graph and its dual.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings |

Pages | 575-587 |

Number of pages | 13 |

DOIs | |

State | Published - Dec 1 2002 |

Event | 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, Canada Duration: Nov 21 2002 → Nov 23 2002 |

### 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 | 2518 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 |
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Country | Canada |

City | Vancouver, BC |

Period | 11/21/02 → 11/23/02 |

### Keywords

- Convex planar drawing
- Graph drawing
- Planar embedding
- Simultaneous embedding

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings*(pp. 575-587). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS). https://doi.org/10.1007/3-540-36136-7_50