Discrete & Computational Geometry

, Volume 27, Issue 3, pp 419–439 | Cite as

On a Conjecture of A. Bezdek

  • R. N. Karasev


The aim of this paper is to prove a conjecture of A. Bezdek. It generalizes conjectures of V. V. Proizvolov. The theorems of this paper are as follows: Suppose points {x i } i=1 p and a polytope X are given. Then we can choose p facets {F i } i=1 p of X so that the convex hulls \conv({x i }\cup F i ) either cover the polytope or do not intersect pairwise in interior points.

Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • R. N. Karasev
    • 1
  1. 1.Department of Mathematics, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia 141700 r_n_karasev@mail.ruRussia

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