More about lower bounds for the number of k-facets

Aichholzer, Oswin and Garcia Lopez de Lacalle, Jesus and Orden Martín, David and Ramos, Pedro (2008). More about lower bounds for the number of k-facets. In: "VI Jornadas de Matemática Discreta y Algorítmica, VI-JMDA", 21/07/2008-23/07/2008, Lérida, España. ISBN 978-84-8409-263-6.

Description

Title: More about lower bounds for the number of k-facets
Author/s:
  • Aichholzer, Oswin
  • Garcia Lopez de Lacalle, Jesus
  • Orden Martín, David
  • Ramos, Pedro
Item Type: Presentation at Congress or Conference (Article)
Event Title: VI Jornadas de Matemática Discreta y Algorítmica, VI-JMDA
Event Dates: 21/07/2008-23/07/2008
Event Location: Lérida, España
Title of Book: Actas de las "VI Jornadas de Matemática Discreta y Algorítmica", VI-JMDA
Date: 8 September 2008
ISBN: 978-84-8409-263-6
Subjects:
Freetext Keywords: (· k)-edges, (· k)-facets, ²-nets
Faculty: E.U. de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this paper we present two results dealing with the number of (• k)-facets of a set of points: •² In R2, we use the notion of ²-net to give structural properties of sets that achieve the optimal lower bound 3¡k+22 ¢ of (• k)-edges for a ¯xed 0 • k • bn=3c ¡ 1;² •In Rd, we show that for k < bn=(d + 1)c the number of (• k)-facets of a set of n points in general position is at least (d + 1)¡k+dd ¢, and that this bound is tight in that range.

More information

Item ID: 4455
DC Identifier: http://oa.upm.es/4455/
OAI Identifier: oai:oa.upm.es:4455
Official URL: http://www.jmda2008.udl.cat/
Deposited by: Memoria Investigacion
Deposited on: 05 Oct 2010 10:03
Last Modified: 20 Apr 2016 13:40
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