Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-Triangles

Authors:
O. Aichholzer;C. Huemer;S. Kappes;B. Speckmann;Cs. D. Tóth
Affiliations:
Graz University of Technology, Institute for Software Technology, Austria;Univ. Poli. de Catalunya, Departament de Matemática Aplicada II, Spain; , Department of Mathematics, TU Berlin, Germany; , Department of Mathematics and Computer Science, TU Eindhoven, Netherland;MIT, Department of Mathematics, 02144, Cambridege, MA, USA
Venue:
Graphs and Combinatorics
Year:
2007

Citing 0
Cited 3

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Abstract

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their complexity. Our upper bounds depend on new Ramsey-type results concerning disjoint empty convex k-gons in point sets.