On some partitioning problems for two-colored point sets

• Clara I. Grima ^[1] ; Carmen Hernando ^[2] ; Clemens Huemer ^[2] ; Ferran Hurtado ^[2]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
  2. [2] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
• Localización: XIII Encuentros de Geometría Computacional: Zaragoza, del 29 de junio al 1 de julio de 2009 / Alfredo García Olaverri (ed. lit.), Javier Tejel Altarriba (ed. lit.), 2009, ISBN 978-84-92774-11-1, págs. 221-228
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let S be a two-colored set of n points in general position in the plane. We show that S admits at least 2 n 17 pairwise disjoint monochromatic triangles with vertices in S and empty of points of S. We further show that S can be partitioned into 3 n 11 subsets with pairwise disjoint convex hull such that within each subset all but at most one point have the same color. A lower bound on the number of subsets needed in any such partition is also given.