Discrete & Computational Geometry

, Volume 48, Issue 3, pp 783–792 | Cite as

Notes About the Carathéodory Number



In this paper we give sufficient conditions for a compactum in ℝn to have Carathéodory number less than n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carathéodory theorem and give a Tverberg-type theorem for families of convex compacta.


Carathéodory’s theorem Helly’s theorem Tverberg’s theorem 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of MathematicsUniversity College LondonLondonEngland
  3. 3.Dept. of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia
  4. 4.Laboratory of Discrete and Computational GeometryYaroslavl State UniversityYaroslavlRussia

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