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Proper Coloring of Geometric Hypergraphs

Authors Balázs Keszegh, Dömötör Pálvölgyi

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Balázs Keszegh
Dömötör Pálvölgyi

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Balázs Keszegh and Dömötör Pálvölgyi. Proper Coloring of Geometric Hypergraphs. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 47:1-47:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.SoCG.2017.47

Abstract

We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then m=3 is sufficient. We prove that when F is the family of all homothetic copies of a given convex polygon, then such an m exists. We also study the problem in higher dimensions.

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Keywords
  • discrete geometry
  • decomposition of multiple coverings
  • geometric hypergraph coloring

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