Combinatorica

, Volume 32, Issue 6, pp 689–702 | Cite as

Analogues of the central point theorem for families with d-intersection property in ℝd

Original paper
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Abstract

In this paper we consider families of compact convex sets in ℝd such that any subfamily of size at most d has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg’s theorem for such families.

Mathematics Subject Classification (2000)

52A20 52A35 52C35 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Laboratory of Discrete and Computational GeometryYaroslavl’ State UniversityYaroslavl’Russia

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