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New results on lower bounds for the number of k-facets
Citation
Aichholzer, Oswin and Garcia Lopez de Lacalle, Jesus and Orden Martín, David and Ramos Alonso, Pedro A. (2008). New results on lower bounds for the number of k-facets. "Electronic Notes In Discrete Mathematics", v. 29 ; pp. 189-193. ISSN 1571-0653. https://doi.org/10.1016/j.endm.2007.07.033.
Description
| Title: | New results on lower bounds for the number of k-facets |
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| Author/s: |
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| Item Type: | Article |
| Título de Revista/Publicación: | Electronic Notes In Discrete Mathematics |
| Date: | August 2008 |
| ISSN: | 1571-0653 |
| Volume: | 29 |
| Subjects: | |
| Freetext Keywords: | (≤ k)-edges, (≤ k)-facets |
| Faculty: | E.U. de Informática (UPM) |
| Department: | Matemática Aplicada |
| Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
Abstract
In this paper we present three different results dealing with the number of (≤ k)- facets of a set of points: (i) We give structural properties of sets in the plane that achieve the optimal lower bound 3_k+2 2 _ of (≤ k)-edges for a fixed k ≤ [n/3 ]− 1; (ii) We show that the new lower bound 3((k+2) 2 ) + 3((k−(n/ 3)+2) 2 ) for the number of (≤ k)-edges of a planar point set is optimal in the range [n/3] ≤ k ≤ [5n/12] − 1; (iii) We show that for k < n/4 the number of (≤ k)-facets of a set of n points in R3 in general position is at least 4((k+3 )3 ), and that this bound is tight in that range.
More information
| Item ID: | 2969 |
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| DC Identifier: | https://oa.upm.es/2969/ |
| OAI Identifier: | oai:oa.upm.es:2969 |
| DOI: | 10.1016/j.endm.2007.07.033 |
| Official URL: | http://www.elsevier.com/wps/find/journaldescription.cws_home/681020/description#description |
| Deposited by: | Memoria Investigacion |
| Deposited on: | 30 Apr 2010 09:31 |
| Last Modified: | 20 Apr 2016 12:34 |
