### 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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Pages | 17-20 |

Number of pages | 4 |

State | Published - Dec 1 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 |
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Country | Canada |

City | Vancouver, BC |

Period | 8/17/09 → 8/19/09 |

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### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology

### Cite this

*Colored simultaneous geometric embeddings and universal pointsets*. 17-20. Paper presented at 21st Annual Canadian Conference on Computational Geometry, CCCG 2009, Vancouver, BC, Canada.