Details

Autor(en) / Beteiligte

• Freij, Ragnar
• Henze, Matthias
• Schmitt, Moritz W.
• Ziegler, Günter M.

Titel

Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs

Ist Teil von

• The Electronic journal of combinatorics, 2013-05, Vol.20 (2)

Erscheinungsjahr

2013

Quelle

EZB Free E-Journals

Beschreibungen/Notizen

• 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.