Journal of Geometry

, Volume 52, Issue 1–2, pp 25–29 | Cite as

On empty convex polytopes

  • Tibor Bisztriczky
  • Heiko Harborth


Letn andd be integers,n>d ≥ 2. We examine the smallest integerg(n,d) such that any setS of at leastg(n,d) points, in general position in Ed, containsn points which are the vertices of an empty convexd-polytopeP, that is, S∩intP = 0. In particular we show thatg(d+k, d) = d+2k−1 for 1 ≤k ≤ iLd/2rL+1.


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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Tibor Bisztriczky
    • 1
  • Heiko Harborth
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Diskrete MathematikTechnische Universität BraunschweigBraunschweigGermany

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