dc.contributor.author Hurtado Díaz, Fernando Alfredo dc.contributor.author Merino, C. dc.contributor.author Oliveros, D. dc.contributor.author Sakai, T. dc.contributor.author Urrutia, J. dc.contributor.author Ventura, Inmaculada dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II dc.date.accessioned 2010-10-11T11:02:54Z dc.date.available 2010-10-11T11:02:54Z dc.date.created 2009-08 dc.date.issued 2009-08 dc.identifier.citation Hurtado, F. [et al.]. On polygons enclosing point sets II. "Graphs and combinatorics", Agost 2009, vol. 25, núm. 3, p. 327-339. dc.identifier.issn 0911-0119 dc.identifier.uri http://hdl.handle.net/2117/9618 dc.description.abstract Let R and B be disjoint point sets such that $R\cup B$ is in general position. We say that B encloses by R if there is a simple polygon P with vertex set B such that all the elements in R belong to the interior of P. In this paper we prove that if the vertices of the convex hull of $R\cup B$ belong to B, and |R| ≤ |Conv(B)| − 1 then B encloses R. The bound is tight. This improves on results of a previous paper in which it was proved that if |R| ≤ 56|Conv (B)| then B encloses R. To obtain our result we prove the next result which is interesting on its own right: Let P be a convex polygon with n vertices $\emph{p_1}$,...,$\emph{p_n}$ and S a set of m points contained in the interior of P, m ≤ n−1. Then there is a convex decomposition {$P_1$,...,$P_n$} of P such that all points from S lie on the boundaries of $P_1$,...,$P_n$, and each $P_i$ contains a whole edge of P on its boundary. dc.format.extent 13 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 Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria dc.subject.lcsh Polygons dc.subject.lcsh Convex geometry dc.subject.lcsh Graph theory dc.title On polygons enclosing point sets II dc.type Article dc.subject.lemac Polígons dc.subject.lemac Geometria convexa 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 10.1007/s00373-009-0848-6 dc.relation.publisherversion http://www.matem.unam.mx/~urrutia/online_papers/EncPointsREV.pdf dc.rights.access Open Access local.identifier.drac 3257540 dc.description.version Postprint (published version) local.citation.author Hurtado, F.; Merino, C.; Oliveros, D.; Sakai, T.; Urrutia, J.; Ventura, I. local.citation.publicationName Graphs and combinatorics local.citation.volume 25 local.citation.number 3 local.citation.startingPage 327 local.citation.endingPage 339
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