Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs

  • Ragnar Freij
  • Matthias Henze
  • Moritz W. Schmitt
  • Günter M. Ziegler
DOI: https://doi.org/10.37236/3315
Keywords: Hansen polytopes, 3^d conjecture, Hanner polytopes, split graphs, threshold graphs

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.
Published
2013-05-16
How to Cite
Freij, R., Henze, M., Schmitt, M. W., & Ziegler, G. M. (2013). Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs. The Electronic Journal of Combinatorics, 20(2), P32. https://doi.org/10.37236/3315
Issue
Volume 20, Issue 2 (2013)
Article Number
P32