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On k-gons and k-holes in point sets
dc.contributor.author | Aichholzer, Oswin |
dc.contributor.author | Fabila Monroy, Ruy |
dc.contributor.author | Gonzalez Aguilar, Hernan |
dc.contributor.author | Hackl, Thomas |
dc.contributor.author | Heredia, Marco A. |
dc.contributor.author | Huemer, Clemens |
dc.contributor.author | Urrutia Galicia, Jorge |
dc.contributor.author | Valtr, Pavel |
dc.contributor.author | Vogtenhuber, Birgit |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-04-13T12:35:46Z |
dc.date.available | 2016-04-13T12:35:46Z |
dc.date.issued | 2015-08-01 |
dc.identifier.citation | Aichholzer, O., Fabila, R., Gonzalez, H., Hackl, T., Heredia, M., Huemer, C., URRUTIA, J., Valtr, P., Vogtenhuber, B. On k-gons and k-holes in point sets. "Computational geometry: theory and applications", 01 Agost 2015, vol. 48, núm. 7, p. 528-537. |
dc.identifier.issn | 0925-7721 |
dc.identifier.uri | http://hdl.handle.net/2117/85613 |
dc.description.abstract | We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show bounds and structural results on maximizing and minimizing their numbers. Most noteworthy, for any k and sufficiently large n, we give a quadratic lower bound for the number of k-holes, and show that this number is maximized by sets in convex position. (C) 2014 Elsevier B.V. All rights reserved. |
dc.format.extent | 10 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Graph theory |
dc.subject.other | Erdos-Szekeres type problems |
dc.subject.other | k-Gons |
dc.subject.other | k-Holes |
dc.subject.other | Empty k-gons |
dc.subject.other | empty convex polygons |
dc.subject.other | lower bounds |
dc.subject.other | number |
dc.title | On k-gons and k-holes in point sets |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1016/j.comgeo.2014.12.007 |
dc.rights.access | Open Access |
local.identifier.drac | 16632698 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Aichholzer, O.; Fabila, R.; Gonzalez, H.; Hackl, T.; Heredia, M.; Huemer, C.; URRUTIA, J.; Valtr, P.; Vogtenhuber, B. |
local.citation.publicationName | Computational geometry: theory and applications |
local.citation.volume | 48 |
local.citation.number | 7 |
local.citation.startingPage | 528 |
local.citation.endingPage | 537 |
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