License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.SoCG.2019.30
URN: urn:nbn:de:0030-drops-104343
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Dumitrescu, Adrian

A Product Inequality for Extreme Distances

LIPIcs-SoCG-2019-30.pdf (0.5 MB)


Let p_1,...,p_n be n distinct points in the plane, and assume that the minimum inter-point distance occurs s_{min} times, while the maximum inter-point distance occurs s_{max} times. It is shown that s_{min} s_{max} <= (9/8)n^2 + O(n); this settles a conjecture of Erdös and Pach (1990).

BibTeX - Entry

  author =	{Adrian Dumitrescu},
  title =	{{A Product Inequality for Extreme Distances}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{30:1--30:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-104343},
  doi =		{10.4230/LIPIcs.SoCG.2019.30},
  annote =	{Keywords: Extreme distances, repeated distances}

Keywords: Extreme distances, repeated distances
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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