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Lower bounds for the number of small convex k-holes
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.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2015-03-11T10:56:59Z |
dc.date.available | 2015-03-11T10:56:59Z |
dc.date.created | 2014-07-01 |
dc.date.issued | 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.issn | 0925-7721 |
dc.identifier.uri | http://hdl.handle.net/2117/26660 |
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. |
dc.format.extent | 9 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | 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.lcsh | Discrete geometry |
dc.subject.lcsh | Combinatorial geometry |
dc.subject.other | Empty convex polygon |
dc.subject.other | Erdos-type problem |
dc.subject.other | Counting |
dc.subject.other | PLANAR POINT SETS |
dc.subject.other | EMPTY |
dc.subject.other | POLYGONS |
dc.subject.other | THEOREM |
dc.title | Lower bounds for the number of small convex k-holes |
dc.type | Article |
dc.subject.lemac | Geometria combinatòria |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1016/j.comgeo.2013.12.002 |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0925772113001703 |
dc.rights.access | Open Access |
local.identifier.drac | 14142440 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Aichholzer, O.; Fabila, R.; Hackl, T.; Huemer, C.; Pilz, A.; Vogtenhuber, B. |
local.citation.publicationName | Computational geometry: theory and applications |
local.citation.volume | 47 |
local.citation.number | 5 |
local.citation.startingPage | 605 |
local.citation.endingPage | 613 |
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