Simple polytopes without small separators, II: Thurston's bound
Metric Geometry
2017-08-23 v1 Combinatorics
Abstract
We show that there are simple 4-dimensional polytopes with n vertices such that all separators of the graph have size at least . This establishes a strong form of a claim by Thurston, for which the construction and proof had been lost. We construct the polytopes by cutting off the vertices and then the edges of a particular type of neighborly cubical polytopes. The graphs of simple polytopes thus obtained are 4-regular; they contain 3-regular "cube-connected cycle graphs" as minors of spanning subgraphs.
Keywords
Cite
@article{arxiv.1708.06718,
title = {Simple polytopes without small separators, II: Thurston's bound},
author = {Lauri Loiskekoski and Günter M. Ziegler},
journal= {arXiv preprint arXiv:1708.06718},
year = {2017}
}
Comments
10 pages, one page of figures