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dc.contributor.authorHurtado Díaz, Fernando Alfredo
dc.contributor.authorMerino, C.
dc.contributor.authorOliveros, D.
dc.contributor.authorSakai, T.
dc.contributor.authorUrrutia, J.
dc.contributor.authorVentura, Inmaculada
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.identifier.citationHurtado, F. [et al.]. On polygons enclosing point sets II. "Graphs and combinatorics", Agost 2009, vol. 25, núm. 3, p. 327-339.
dc.description.abstractLet 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.extent13 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject.lcshConvex geometry
dc.subject.lcshGraph theory
dc.titleOn polygons enclosing point sets II
dc.subject.lemacGeometria convexa
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
upcommons.citation.authorHurtado, F.; Merino, C.; Oliveros, D.; Sakai, T.; Urrutia, J.; Ventura, I.
upcommons.citation.publicationNameGraphs and combinatorics

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