Lower bounds for the number of small convex k-holes

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/26660

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.contributor	Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.contributor.author	Aichholzer, Oswin
dc.contributor.author	Fabila Monroy, Ruy
dc.contributor.author	Hackl, Thomas
dc.contributor.author	Huemer, Clemens
dc.contributor.author	Pilz, Alexander
dc.contributor.author	Vogtenhuber, Birgit
dc.date	2014-07-01
dc.identifier.citation	Aichholzer, 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.citation	0925-7721
dc.identifier.citation	10.1016/j.comgeo.2013.12.002
dc.identifier.uri	http://hdl.handle.net/2117/26660
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science/article/pii/S0925772113001703
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
dc.subject	Discrete geometry
dc.subject	Combinatorial geometry
dc.subject	Empty convex polygon
dc.subject	Erdos-type problem
dc.subject	Counting
dc.subject	PLANAR POINT SETS
dc.subject	EMPTY
dc.subject	POLYGONS
dc.subject	THEOREM
dc.subject	Geometria combinatòria
dc.title	Lower bounds for the number of small convex k-holes
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	Let 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.

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