Universal point sets for 2-coloured trees

Authors:
Mereke van Garderen;Giuseppe Liotta;Henk Meijer
Affiliations:
Technical University Eindhoven, The Netherlands;Universití di Perugia, Italy;Roosevelt Academy, The Netherlands
Venue:
Information Processing Letters
Year:
2012

Citing 5
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Point-set embeddings of trees with given partial drawings

Computational Geometry: Theory and Applications
Colored Simultaneous Geometric Embeddings and Universal Pointsets

Algorithmica - Special issue: Algorithms, Combinatorics, & Geometry

Point-Set embeddability of 2-colored trees

GD'12 Proceedings of the 20th international conference on Graph Drawing

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Abstract

Let R and B be two sets of distinct points such that the points of R are coloured red and the points of B are coloured blue. Let G be a family of planar graphs such that for each graph in the family |R| vertices are red and |B| vertices are blue. The set R@?B is a universal point set for G if every graph G@?G has a straight-line planar drawing such that the blue vertices of G are mapped to the points of B and the red vertices of G are mapped to the points of R. In this paper we describe universal point sets for meaningful classes of 2-coloured trees and show applications of these results to the coloured simultaneous geometric embeddability problem.