## Abstract

In a convex grid drawing of a plane graph, every edge is drawn as a straight-line segment without any edge-intersection, every vertex is located at a grid point, and every facial cycle is drawn as a convex polygon. A plane graph G has a convex drawing if and only if G is internally triconnected. It has been known that an internally triconnected plane graph G of n vertices has a convex grid drawing on a grid of O(n ^{3}) area if the triconnected component decomposition tree of G has at most four leaves. In this paper, we improve the area bound O(n ^{3}) to O(n ^{2}), which is optimal up to a constant factor. More precisely, we show that G has a convex grid drawing on a 2n×4n grid. We also present an algorithm to find such a drawing in linear time.

Original language | English |
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Title of host publication | Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings |

Pages | 760-770 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 2009 |

Event | 20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States Duration: 2009 Dec 16 → 2009 Dec 18 |

### 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 | 5878 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 20th International Symposium on Algorithms and Computation, ISAAC 2009 |
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Country/Territory | United States |

City | Honolulu, HI |

Period | 09/12/16 → 09/12/18 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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