Abstract
Kalai and Kleitman [Bull. Amer. Math. Soc. (N.S.), 26 (1992), pp. 315--316] established the bound $n^{\log(d) + 2}$ for the diameter of a $d$-dimensional polyhedron with $n$ facets. Here we improve the bound slightly to $(n-d)^{\log(d)}$.
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