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