Face numbers of centrally symmetric polytopes from split graphs

2012/01/27 by Freij, Ragnar, Henze, Matthias, Schmitt, Moritz W. +1 · 1 citation
#05C17 #52B05 #52B12 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1201.5790

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.

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