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.2020.1
URN: urn:nbn:de:0030-drops-121591
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12159/
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Ackerman, Eyal ; Keszegh, Balázs ; Rote, Günter

An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons

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LIPIcs-SoCG-2020-1.pdf (1 MB)


Abstract

What is the maximum number of intersections of the boundaries of a simple m-gon and a simple n-gon, assuming general position? This is a basic question in combinatorial geometry, and the answer is easy if at least one of m and n is even. If both m and n are odd, the best known construction has mn-(m+n)+3 intersections, and it is conjectured that this is the maximum. However, the best known upper bound is only mn-(m + ⌈ n/6 ⌉), for m ≥ n. We prove a new upper bound of mn-(m+n)+C for some constant C, which is optimal apart from the value of C.

BibTeX - Entry

@InProceedings{ackerman_et_al:LIPIcs:2020:12159,
  author =	{Eyal Ackerman and Bal{\'a}zs Keszegh and G{\"u}nter Rote},
  title =	{{An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{1:1--1:18},
  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/2020/12159},
  URN =		{urn:nbn:de:0030-drops-121591},
  doi =		{10.4230/LIPIcs.SoCG.2020.1},
  annote =	{Keywords: Simple polygon, Ramsey theory, combinatorial geometry}
}

Keywords: Simple polygon, Ramsey theory, combinatorial geometry
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020


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