On the Minimum Size of a Point Set Containing Two Non-intersecting Empty Convex Polygons

  • Kiyoshi Hosono
  • Masatsugu Urabe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)


Let n (k, l) be the smallest integer such that any set of n (k, l) points in the plane, no three collinear, contains both an empty convex k -gon and an empty convex l -gon, which do not intersect. We show that n (3,5) = 10, 12 ≤ n (4,5) ≤ 14, 16 ≤ n (5,5) ≤ 20.


Minimum Size Convex Cone Small Integer Convex Region Attack Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kiyoshi Hosono
    • 1
  • Masatsugu Urabe
    • 1
  1. 1.Department of MathematicsTokai UniversityShizuokaJapan

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