On the Diameter of Lattice Polytopes

In this paper we show that the diameter of a d -dimensional lattice polytope in [0,k]^n is at most ⌊( k-1/2) d⌋ . This result implies that the diameter of a d -dimensional half-integral polytope is at most ⌊3/2 d⌋ . We also show that for half-integral polytopes the latter bound is tight for any d .