English

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

R2 v1 2026-06-21T20:10:39.682Z