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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.authorValtr, Pavel
dc.contributor.authorVogtenhuber, Birgit
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2016-04-13T12:35:46Z
dc.date.available2016-04-13T12:35:46Z
dc.date.issued2015-08-01
dc.identifier.citationAichholzer, 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.issn0925-7721
dc.identifier.urihttp://hdl.handle.net/2117/85613
dc.description.abstractWe 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.extent10 p.
dc.language.isoeng
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshGraph theory
dc.subject.otherErdos-Szekeres type problems
dc.subject.otherk-Gons
dc.subject.otherk-Holes
dc.subject.otherEmpty k-gons
dc.subject.otherempty convex polygons
dc.subject.otherlower bounds
dc.subject.othernumber
dc.titleOn k-gons and k-holes in point sets
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.identifier.doi10.1016/j.comgeo.2014.12.007
dc.rights.accessOpen Access
drac.iddocument16632698
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorAichholzer, O., Fabila, R., Gonzalez, H., Hackl, T., Heredia, M., Huemer, C., URRUTIA, J., Valtr, P., Vogtenhuber, B.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameComputational geometry: theory and applications
upcommons.citation.volume48
upcommons.citation.number7
upcommons.citation.startingPage528
upcommons.citation.endingPage537


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