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dc.contributor.authorAichholzer, Oswin
dc.contributor.authorFabila Monroy, Ruy
dc.contributor.authorHackl, Thomas
dc.contributor.authorHuemer, Clemens
dc.contributor.authorPilz, Alexander
dc.contributor.authorVogtenhuber, Birgit
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2015-03-11T10:56:59Z
dc.date.available2015-03-11T10:56:59Z
dc.date.created2014-07-01
dc.date.issued2014-07-01
dc.identifier.citationAichholzer, O. [et al.]. Lower bounds for the number of small convex k-holes. "Computational geometry: theory and applications", 01 Juliol 2014, vol. 47, núm. 5, p. 605-613.
dc.identifier.issn0925-7721
dc.identifier.urihttp://hdl.handle.net/2117/26660
dc.description.abstractLet S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds on h(k)(n), for 3 <= k <= 5. Specifically, we show that h(3)(n) >= n(2) - 32n/7 + 22/7, h(4)(n) >= n(2)/2 - 9n/4 - o(n), and h(5)(n) >= 3n/4 - o(n). We further settle several questions on sets of 12 points posed by Dehnhardt in 1987. (C) 2013 Elsevier B.V. All rights reserved.
dc.format.extent9 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
dc.subject.lcshDiscrete geometry
dc.subject.lcshCombinatorial geometry
dc.subject.otherEmpty convex polygon
dc.subject.otherErdos-type problem
dc.subject.otherCounting
dc.subject.otherPLANAR POINT SETS
dc.subject.otherEMPTY
dc.subject.otherPOLYGONS
dc.subject.otherTHEOREM
dc.titleLower bounds for the number of small convex k-holes
dc.typeArticle
dc.subject.lemacGeometria combinatòria
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.identifier.doi10.1016/j.comgeo.2013.12.002
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0925772113001703
dc.rights.accessOpen Access
local.identifier.drac14142440
dc.description.versionPostprint (author’s final draft)
local.citation.authorAichholzer, O.; Fabila, R.; Hackl, T.; Huemer, C.; Pilz, A.; Vogtenhuber, B.
local.citation.publicationNameComputational geometry: theory and applications
local.citation.volume47
local.citation.number5
local.citation.startingPage605
local.citation.endingPage613


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