Three-chromatic geometric hypergraphs

  • Gábor Damásdi

    Eötvös Loránd University, Budapest, Hungary
  • Dömötör Pálvölgyi

    Eötvös Loránd University, Budapest, Hungary
Three-chromatic geometric hypergraphs cover

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Abstract

We prove that for any planar convex body there is a positive integer with the property that any finite point set in the plane can be three-colored in such a way that no translate of contains points of  (or more), 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. The extended abstract of this paper already appeared in the proceedings of SoCG ’22.

Cite this article

Gábor Damásdi, Dömötör Pálvölgyi, Three-chromatic geometric hypergraphs. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1516