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Face numbers of centrally symmetric polytopes from split graphs

Please always quote using this URN:urn:nbn:de:0296-matheon-10318
  • 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.

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Metadaten
Author:Ragnar Freij, Matthias Henze, Moritz W. Schmitt, Günter M. Ziegler
URN:urn:nbn:de:0296-matheon-10318
Referee:Martin Skutella
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/27
Release Date:2012/01/27
Tag:face numbers of polytopes
Institute:Research Center Matheon
Freie Universität Berlin
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B12 Special polytopes (linear programming, centrally symmetric, etc.)
Preprint Number:900
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