English

Simple polytopes without small separators

Metric Geometry 2015-10-05 v1 Combinatorics

Abstract

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/log3/2n)\Omega(n/\log^{3/2}n). This disproves a conjecture by Kalai from 1991/2004.

Keywords

Cite

@article{arxiv.1510.00511,
  title  = {Simple polytopes without small separators},
  author = {Lauri Loiskekoski and Günter M. Ziegler},
  journal= {arXiv preprint arXiv:1510.00511},
  year   = {2015}
}

Comments

7 pages

R2 v1 2026-06-22T11:11:05.281Z