An upper bound for the diameter of a polytope

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Abstract

The distance between two vertices of a polytope is the minimum number of edges in a path joining them. The diameter of a polytope is the greatest distance between two vertices of the polytope. We show that if P is a d-dimensional polytope with n facets, then the diameter of P is at most 132d−3(n−d+52).

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Research supported by a Sloan Foundation grant.