License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2020.60
URN: urn:nbn:de:0030-drops-122183
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12218/
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Pálvölgyi, Dömötör

Radon Numbers Grow Linearly

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LIPIcs-SoCG-2020-60.pdf (0.4 MB)

Abstract

Define the k-th Radon number r_k of a convexity space as the smallest number (if it exists) for which any set of r_k points can be partitioned into k parts whose convex hulls intersect. Combining the recent abstract fractional Helly theorem of Holmsen and Lee with earlier methods of Bukh, we prove that r_k grows linearly, i.e., r_k ≤ c(r₂)⋅ k.

BibTeX - Entry

@InProceedings{plvlgyi:LIPIcs:2020:12218,
  author =	{D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi},
  title =	{{Radon Numbers Grow Linearly}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{60:1--60:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12218},
  URN =		{urn:nbn:de:0030-drops-122183},
  doi =		{10.4230/LIPIcs.SoCG.2020.60},
  annote =	{Keywords: discrete geometry, convexity space, Radon number}
}

Keywords: discrete geometry, convexity space, Radon number
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020

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