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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

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • 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