DROPS

Document

DOI: 10.4230/LIPIcs.SoCG.2022.32

Three-Chromatic Geometric Hypergraphs

Authors: Gábor Damásdi and Dömötör Pálvölgyi

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

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.

Cite as

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)

Copy BibTex To Clipboard

@InProceedings{damasdi_et_al:LIPIcs.SoCG.2022.32,
  author =	{Dam\'{a}sdi, G\'{a}bor and P\'{a}lv\"{o}lgyi, D\"{o}m\"{o}t\"{o}r},
  title =	{{Three-Chromatic Geometric Hypergraphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.32},
  URN =		{urn:nbn:de:0030-drops-160401},
  doi =		{10.4230/LIPIcs.SoCG.2022.32},
  annote =	{Keywords: Discrete geometry, Geometric hypergraph coloring, Decomposition of multiple coverings}
}

Search Results

Documents authored by Damásdi, Gábor

Three-Chromatic Geometric Hypergraphs

Abstract

Cite as

Thanks for your feedback!

Could not send message