### Abstract

We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n ^{2}) × O(n ^{2}) grid, with at most three bends per edge, where n is the number of vertices. For the case when the input graphs are both trees, only one bend per edge is required. We also describe an O(n) time algorithm for simultaneous embedding with fixed-edges for tree-path pairs on the O(n) × O(n ^{2}) grid with at most one bend per tree-edge and no bends along path edges.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science |

Editors | J. Pach |

Pages | 195-205 |

Number of pages | 11 |

Volume | 3383 |

State | Published - 2004 |

Event | 12th International Symposium on Graph Drawing, GD 2004 - New York, NY, United States Duration: Sep 29 2004 → Oct 2 2004 |

### Other

Other | 12th International Symposium on Graph Drawing, GD 2004 |
---|---|

Country | United States |

City | New York, NY |

Period | 9/29/04 → 10/2/04 |

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3383, pp. 195-205)

**Simultaneous embedding of planar graphs with few bends.** / Erten, Cesim; Kobourov, Stephen G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science.*vol. 3383, pp. 195-205, 12th International Symposium on Graph Drawing, GD 2004, New York, NY, United States, 9/29/04.

}

TY - GEN

T1 - Simultaneous embedding of planar graphs with few bends

AU - Erten, Cesim

AU - Kobourov, Stephen G

PY - 2004

Y1 - 2004

N2 - We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n 2) × O(n 2) grid, with at most three bends per edge, where n is the number of vertices. For the case when the input graphs are both trees, only one bend per edge is required. We also describe an O(n) time algorithm for simultaneous embedding with fixed-edges for tree-path pairs on the O(n) × O(n 2) grid with at most one bend per tree-edge and no bends along path edges.

AB - We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n 2) × O(n 2) grid, with at most three bends per edge, where n is the number of vertices. For the case when the input graphs are both trees, only one bend per edge is required. We also describe an O(n) time algorithm for simultaneous embedding with fixed-edges for tree-path pairs on the O(n) × O(n 2) grid with at most one bend per tree-edge and no bends along path edges.

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UR - http://www.scopus.com/inward/citedby.url?scp=24144437166&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3383

SP - 195

EP - 205

BT - Lecture Notes in Computer Science

A2 - Pach, J.

ER -