Decompositions, partitions, and coverings with convex polygons and pseudo-triangles

O. Aichholzer, C. Huemer, S. Kappes, B. Speckmann, Cs.D. Tóth

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)481-507
JournalGraphs and Combinatorics
Volume23
Issue number5
DOIs
Publication statusPublished - 2007

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