Israel Journal of Mathematics

, Volume 221, Issue 2, pp 731–739 | Cite as

Simple polytopes without small separators

  • Lauri Loiskekoski
  • Günter M. Ziegler


We show that by cutting off the vertices and then the edges of neighborly cubical polytopes, one obtains simple 4-dimensional polytopes with n vertices such that all separators of the graph have size at least Ω(n/log3/2 n). This disproves a conjecture by Kalai from 1991/2004.


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Copyright information

© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Institut für MathematikFU BerlinBerlinGermany

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