## Abstract

In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It is known that every planar graph G of n vertices has a grid drawing on an (n - 2) × (n - 2) or (4n/3) × (2n/3) integer grid. In this paper we show that if a planar graph G has a balanced partition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G1 and G _{2}, then G has a max{n _{1},n _{2}} × max{n _{1},n _{2}} grid drawing, where n _{1} and n _{2} are the numbers of vertices in G _{1} and G _{2}, respectively. In particular, we show that every series-parallel graph G has a (2n/3) × (2n/3) grid drawing and a grid drawing with area smaller than 0.3941n ^{2} (< (2/3) ^{2}n ^{2}).

Original language | English |
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Pages (from-to) | 99-115 |

Number of pages | 17 |

Journal | Journal of Combinatorial Optimization |

Volume | 24 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Aug |

## Keywords

- Grid drawing
- Partition
- Planar graph
- Series-parallel graph

## ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics