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 Citació: Hurtado, F. [et al.]. On polygons enclosing point sets II. "Graphs and combinatorics", Agost 2009, vol. 25, núm. 3, p. 327-339. Títol: On polygons enclosing point sets II Autor: Hurtado Díaz, Fernando Alfredo ; Merino, C.; Oliveros, D.; Sakai, T.; Urrutia, J.; Ventura, Inmaculada Data: ago-2009 Tipus de document: Article Resum: 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. ISSN: 0911-0119 URI: http://hdl.handle.net/2117/9618 DOI: 10.1007/s00373-009-0848-6 Versió de l'editor: http://www.matem.unam.mx/~urrutia/online_papers/EncPointsREV.pdf Apareix a les col·leccions: DCCG - Grup de recerca en geometria computacional, combinatoria i discreta. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revistaAltres. Enviament des de DRAC Comparteix: