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.
Author: | Ragnar Freij, Matthias Henze, Moritz W. Schmitt, Günter M. Ziegler |
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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 |