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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12159/
Ackerman, Eyal ;
Keszegh, Balázs ;
Rote, Günter
An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons
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 |
