### Abstract

A simultaneous embedding of two vertex-labeled planar graphs on n vertices is possible if there exists a labeled point set of size n such that each of the graphs can be realized on that point set without crossings. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.

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

Pages (from-to) | 173-182 |

Number of pages | 10 |

Journal | Computational Geometry: Theory and Applications |

Volume | 42 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2009 |

### Fingerprint

### Keywords

- Simultaneous embedding

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*42*(2), 173-182. https://doi.org/10.1016/j.comgeo.2008.05.003

**Simultaneous graph embedding with bends and circular arcs.** / Cappos, Justin; Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Kobourov, Stephen G.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 42, no. 2, pp. 173-182. https://doi.org/10.1016/j.comgeo.2008.05.003

}

TY - JOUR

T1 - Simultaneous graph embedding with bends and circular arcs

AU - Cappos, Justin

AU - Estrella-Balderrama, Alejandro

AU - Fowler, J. Joseph

AU - Kobourov, Stephen G.

PY - 2009/2

Y1 - 2009/2

N2 - A simultaneous embedding of two vertex-labeled planar graphs on n vertices is possible if there exists a labeled point set of size n such that each of the graphs can be realized on that point set without crossings. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.

AB - A simultaneous embedding of two vertex-labeled planar graphs on n vertices is possible if there exists a labeled point set of size n such that each of the graphs can be realized on that point set without crossings. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.

KW - Simultaneous embedding

UR - http://www.scopus.com/inward/record.url?scp=84867931153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867931153&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2008.05.003

DO - 10.1016/j.comgeo.2008.05.003

M3 - Article

AN - SCOPUS:84867931153

VL - 42

SP - 173

EP - 182

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 2

ER -