A superlinear lower bound on the number of 5-holes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10360667" target="_blank" >RIV/00216208:11320/17:10360667 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2017.8" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.SoCG.2017.8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2017.8" target="_blank" >10.4230/LIPIcs.SoCG.2017.8</a>
Alternative languages
Result language
angličtina
Original language name
A superlinear lower bound on the number of 5-holes
Original language description
Let P be a finite set of points in the plane in general position, that is, no three points of P are on a common line. We say that a set H of five points from P is a 5-hole in P if H is the vertex set of a convex 5-gon containing no other points of P. For a positive integer n, let h_5(n) be the minimum number of 5-holes among all sets of n points in the plane in general position. We show that h_5(n) = Omega(n log^{4/5} n), obtaining the first superlinear lower bound on h_5(n). The following structural result, which might be of independent interest, is a crucial step in the proof of this lower bound. If a finite set P of points in the plane in general position is partitioned by a line l into two subsets, each of size at least 5 and not in convex position, then l intersects the convex hull of some 5-hole in P. The proof of this result is computer-assisted.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
33rd International Symposium on Computational Geometry (SoCG 2017)
ISBN
978-3-95977-038-5
ISSN
1868-8969
e-ISSN
neuvedeno
Number of pages
16
Pages from-to
1-16
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Brisbane
Event date
Jul 4, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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