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A Note on the Number of Empty Triangles

  • Alfredo García
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

Let P be a set of n points on the plane, in general position, H of them placed on the boundary of the convex hull of P. In this note we prove that there is a well defined family of empty triangles, the family of empty triangles not generated by an empty convex pentagon, containing exactly n2 − 5n + H + 4 empty triangles. This result immediately implies a slight improvement on the lower bound on the number of empty triangles that every set of n points in the plane must determine.

Keywords

Empty triangle empty convex pentagon convex hull points in general position 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alfredo García
    • 1
  1. 1.Departamento de Métodos Estadísticos and IUMAUniversidad de ZaragozaZaragozaSpain

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