On the Diameter of Lattice Polytopes

Abstract

In this paper we show that the diameter of a d-dimensional lattice polytope in $$[0,k]^n$$[0,k]n is at most $${\lfloor }{\left( k-\frac{1}{2}\right) d}{\rfloor }$$?k-12d?. This result implies that the diameter of a d-dimensional half-integral polytope is at most $${\lfloor }{\frac{3}{2} d}{\rfloor }$$?32d?. We also show that for half-integral polytopes the latter bound is tight for any d.