Colored Simultaneous Geometric Embeddings and Universal Pointsets

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 caterpillars, 3-colored radius-2 stars, and 2-colored spiders.

• Type: Conference
• Year: 2009
• Where: CCCG
• Authors: Alejandro Estrella-Balderrama, J. Joseph Fowler, Stephen G. Kobourov
• Keywords: CCCG 2007, CCCG 2009, Simultaneous Geometric Embedding, Straight-line Plane Drawing, Universal Pointsets