### Abstract

A set of n points in the plane is a universal pointset for a given class of graphs, if any n-vertex graph in that class can be embedded in the plane so that vertices are mapped to points, edges are drawn with straight lines, and there are no crossings. A set of graphs defined on the same n vertices, which are partitioned into k colors, has a colored simultaneous geometric embedding if there exists a set of k-colored points in the plane such that each vertex can be mapped to a point of the same color, resulting in a straight-line plane drawing of each graph. We consider classes of trees and show that there exist universal or near universal pointsets for 3-colored cater- pillars, 3-colored radius-2 stars, and 2-colored spiders.

Original language | English (US) |
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Title of host publication | Proceedings of the 21st Annual Canadian Conference on Computational Geometry, CCCG 2009 |

Pages | 17-20 |

Number of pages | 4 |

State | Published - 2009 |

Externally published | Yes |

Event | 21st Annual Canadian Conference on Computational Geometry, CCCG 2009 - Vancouver, BC, Canada Duration: Aug 17 2009 → Aug 19 2009 |

### Other

Other | 21st Annual Canadian Conference on Computational Geometry, CCCG 2009 |
---|---|

Country | Canada |

City | Vancouver, BC |

Period | 8/17/09 → 8/19/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology

### Cite this

*Proceedings of the 21st Annual Canadian Conference on Computational Geometry, CCCG 2009*(pp. 17-20)

**Colored simultaneous geometric embeddings and universal pointsets.** / Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Kobourov, Stephen G.

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

*Proceedings of the 21st Annual Canadian Conference on Computational Geometry, CCCG 2009.*pp. 17-20, 21st Annual Canadian Conference on Computational Geometry, CCCG 2009, Vancouver, BC, Canada, 8/17/09.

}

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T1 - Colored simultaneous geometric embeddings and universal pointsets

AU - Estrella-Balderrama, Alejandro

AU - Fowler, J. Joseph

AU - Kobourov, Stephen G

PY - 2009

Y1 - 2009

N2 - A set of n points in the plane is a universal pointset for a given class of graphs, if any n-vertex graph in that class can be embedded in the plane so that vertices are mapped to points, edges are drawn with straight lines, and there are no crossings. A set of graphs defined on the same n vertices, which are partitioned into k colors, has a colored simultaneous geometric embedding if there exists a set of k-colored points in the plane such that each vertex can be mapped to a point of the same color, resulting in a straight-line plane drawing of each graph. We consider classes of trees and show that there exist universal or near universal pointsets for 3-colored cater- pillars, 3-colored radius-2 stars, and 2-colored spiders.

AB - A set of n points in the plane is a universal pointset for a given class of graphs, if any n-vertex graph in that class can be embedded in the plane so that vertices are mapped to points, edges are drawn with straight lines, and there are no crossings. A set of graphs defined on the same n vertices, which are partitioned into k colors, has a colored simultaneous geometric embedding if there exists a set of k-colored points in the plane such that each vertex can be mapped to a point of the same color, resulting in a straight-line plane drawing of each graph. We consider classes of trees and show that there exist universal or near universal pointsets for 3-colored cater- pillars, 3-colored radius-2 stars, and 2-colored spiders.

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M3 - Conference contribution

SP - 17

EP - 20

BT - Proceedings of the 21st Annual Canadian Conference on Computational Geometry, CCCG 2009

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