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Three-Chromatic Geometric Hypergraphs

Authors Gábor Damásdi , Dömötör Pálvölgyi

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Author Details

Gábor Damásdi
  • MTA-ELTE Lendület Combinatorial Geometry Research Group, Dept. of Computer Science, ELTE Eötvös Loránd University, Budapest, Hungary
Dömötör Pálvölgyi
  • MTA-ELTE Lendület Combinatorial Geometry Research Group, Dept. of Computer Science, ELTE Eötvös Loránd University, Budapest, Hungary

Funding

  • Damásdi, Gábor: Supported by the ÚNKP-21-3 New National Excellence Program of the Ministry for Innovation and Technology from the source of the National Research, Development and Innovation Fund, and both researchers supported by the Lendület program of the Hungarian Academy of Sciences (MTA), under grant number LP2017-19/2017.

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Gábor Damásdi and Dömötör Pálvölgyi. Three-Chromatic Geometric Hypergraphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 32:1-32:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SoCG.2022.32

Abstract

We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no translate of C containing at least m points of P, all of the same color. As a part of the proof, we show a strengthening of the Erdős-Sands-Sauer-Woodrow conjecture. Surprisingly, the proof also relies on the two dimensional case of the Illumination conjecture.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Hypergraphs
Keywords
  • Discrete geometry
  • Geometric hypergraph coloring
  • Decomposition of multiple coverings

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References

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