Making triangles colorful

Authors

  • Jean Cardinal ULB, Brussels, Belgium
  • Kolja Knauer Université Montpellier 2
  • Piotr Micek Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University Krakow
  • Torsten Ueckerdt Department of Mathematics Karlsruhe Institute of Technology Karlsruhe

DOI:

https://doi.org/10.20382/jocg.v4i1a10

Abstract

We prove that for any point set P in the plane, a triangle T, and a positive integer k, there exists a coloring of P with k colors such that any homothetic copy of T containing at least 144k8 points of P contains at least one of each color. This is the first polynomial bound for range spaces induced by homothetic polygons.The only previously known bound for this problem applies to the more general case of octants in ℝ3, but is doubly exponential.

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Author Biography

Jean Cardinal, ULB, Brussels, Belgium

Associate Prof.

Computer Science Dept.

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Published

2013-12-23

How to Cite

Cardinal, Jean, Kolja Knauer, Piotr Micek, and Torsten Ueckerdt. 2013. “Making Triangles Colorful”. Journal of Computational Geometry 4 (1):240–246. https://doi.org/10.20382/jocg.v4i1a10.

Issue

Vol. 4 No. 1 (2013)

Section

Articles

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