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dc.contributor.authorAichholzer, Oswin
dc.contributor.authorFabila Monroy, Ruy
dc.contributor.authorGonzalez Aguilar, Hernan
dc.contributor.authorHackl, Thomas
dc.contributor.authorHeredia, Marco A.
dc.contributor.authorHuemer, Clemens
dc.contributor.authorUrrutia Galicia, Jorge
dc.contributor.authorVogtenhuber, Birgit
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2015-03-11T10:45:04Z
dc.date.available2015-03-11T10:45:04Z
dc.date.created2014-08-01
dc.date.issued2014-08-01
dc.identifier.citationAichholzer, O. [et al.]. 4-Holes in point sets. "Computational geometry: theory and applications", 01 Agost 2014, vol. 47, núm. 6, p. 644-650.
dc.identifier.issn0925-7721
dc.identifier.urihttp://hdl.handle.net/2117/26659
dc.description.abstractWe consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and minimizing the number of general 4-holes, and maximizing the number of non-convex 4-holes. In particular, we show that for n >= 9, the maximum number of general 4-holes is ((pi)(4)); the minimum number of general 4-holes is at least 5/2 n(2) - circle minus(n); and the maximum number of non-convex 4-holes is at least 1/2 n(3) - circle minus(n(2) logn) and at most 1/2 n(3) - circle minus(n(2)). 2014 (c) Elsevier B.V. All rights reserved.
dc.format.extent7 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::Matemàtica discreta
dc.subject.lcshComputer science--Mathematics
dc.subject.otherErdos-Szekeres type problems
dc.subject.otherk-Holes
dc.subject.otherEmpty k-gons
dc.subject.otherEmpty convex polygons
dc.subject.otherTheorem
dc.subject.otherNumber
dc.title4-Holes in point sets
dc.typeArticle
dc.subject.lemacInformàtica -- Matemàtica
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.identifier.doi10.1016/j.comgeo.2013.12.004
dc.rights.accessOpen Access
drac.iddocument14576303
dc.description.versionPostprint (author’s final draft)
upcommons.citation.authorAichholzer, O.; Fabila, R.; Gonzalez, H.; Hackl, T.; Heredia, M.; Huemer, C.; URRUTIA, J.; Vogtenhuber, B.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameComputational geometry: theory and applications
upcommons.citation.volume47
upcommons.citation.number6
upcommons.citation.startingPage644
upcommons.citation.endingPage650


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