Discrete & Computational Geometry

, Volume 24, Issue 2–3, pp 345–354 | Cite as

Transversals for Families of Translates of a Two-Dimensional Convex Compact Set

  • R. N. Karasev


The following Theorem 1 gives an affirmative answer to Grünbaum's old question. Let F be a family of translates of a convex compact set KR 2 . If every two elements of F have a common point, then there exist three points A, B, C ∈R 2 such that every element of F contains some of these points.


Common Point Convex Compact Affirmative Answer 
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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • R. N. Karasev
    • 1
  1. 1.Yaroslavl State University, Sovetskaya Str. 14, Yaroslavl 150000, Russia r_n_karasev@mail.ruRU

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