Face numbers of centrally symmetric polytopes from split graphs
Metric Geometry
2012-01-30 v1 Combinatorics
Abstract
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3^d-conjecture for such polytopes (they all have at least 3^d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3^d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.
Keywords
Cite
@article{arxiv.1201.5790,
title = {Face numbers of centrally symmetric polytopes from split graphs},
author = {Ragnar Freij and Matthias Henze and Moritz W. Schmitt and Günter M. Ziegler},
journal= {arXiv preprint arXiv:1201.5790},
year = {2012}
}
Comments
10 pages, 1 figure