Opened Access Quadrangulations and 2-Colorations
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Author: Cortés Parejo, María del Carmen
Márquez Pérez, Alberto
Nakamoto, Atsuhiro
Valenzuela Muñoz, Jesús
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2005
Published in: Proceedings of the 21st European Workshop on Computational Geometry, Eindhoven, The Netherlands, March 9-11, 2005, p.65-68
Document type: Presentation
Abstract: Any metric quadrangulation (made by segments of straight line) of a point set in the plane determines a 2-coloration of the set, such that edges of the quadrangulation can only join points with different colors. In this work we focus in 2-colorations and study whether they admit a quadrangulation or not, and whether, given two quadrangulations of the same 2-coloration, it is possible to carry one into the other using some local operations, called diagonal slides and diagonal rotation. Although the answer is negative in general, we can show a very wide family of 2-colorations, called onions 2-coloration, that are quadrangulable and which graph of quadrangulations is always connected.
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