# diameter

## Average diameter of a bounded cell of a simple arrangement ★★

Author(s): Deza; Terlaky; Zinchenko

\begin{conjecture} The average diameter of a bounded cell of a simple arrangement defined by $n$ hyperplanes in dimension $d$ is not greater than $d$. \end{conjecture}

Keywords: arrangement; diameter; polytope

## Hirsch Conjecture ★★★

Author(s): Hirsch

\begin{conjecture} Let $P$ be a convex $d$-\Def{polytope} with $n$ \Def[facets]{Facet_(mathematics)}. Then the diameter of the graph of the polytope $P$ is at most $n-d$. \end{conjecture}