Günter Rote:

An Upper Bound on the Number of Facets of a 0-1-Polytope

Draft, December 1996, 3 pages


A 0-1-polytope in d dimensions has at most 6.4*d!/sqrt(d) facets.
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Volker Kaibel has recently (August 1997) shown a better bound of 2*(d-1)! by a very simple argument. Tamás Fleiner has further improved the bound to O((d-2)!) (September 1997). A list of the best lower bounds for the number of facets is maintained by Ulrich Kortenkamp.