Face numbers of centrally symmetric polytopes from split graphs
Abstract
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3d-conjecture for such polytopes (they all have at least 3d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3d+16 nonempty faces.
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