### Abstract

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. In particular, given a mapping, we show how to embed two paths on an n x n grid, and two caterpillar graphs on a 3n x 3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) x O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n ^{2}) x O(n ^{2}) grid.

Original language | English (US) |
---|---|

Pages (from-to) | 243-255 |

Number of pages | 13 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2748 |

State | Published - 2003 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*2748*, 243-255.

**On simultaneous planar graph embeddings.** / Brass, P.; Cenek, E.; Duncan, Christian A.; Efrat, Alon; Erten, C.; Ismailescu, D.; Kobourov, Stephen G; Lubiw, A.; Mitchell, J. S B.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2748, pp. 243-255.

}

TY - JOUR

T1 - On simultaneous planar graph embeddings

AU - Brass, P.

AU - Cenek, E.

AU - Duncan, Christian A.

AU - Efrat, Alon

AU - Erten, C.

AU - Ismailescu, D.

AU - Kobourov, Stephen G

AU - Lubiw, A.

AU - Mitchell, J. S B

PY - 2003

Y1 - 2003

N2 - We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. In particular, given a mapping, we show how to embed two paths on an n x n grid, and two caterpillar graphs on a 3n x 3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) x O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n 2) x O(n 2) grid.

AB - We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. In particular, given a mapping, we show how to embed two paths on an n x n grid, and two caterpillar graphs on a 3n x 3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) x O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n 2) x O(n 2) grid.

UR - http://www.scopus.com/inward/record.url?scp=35248879254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248879254&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:35248879254

VL - 2748

SP - 243

EP - 255

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -