The diameter range conjecture for transportation polytopes

For positive integers $p$ and $q$, consider the graph diameter of a $p \times q$ transportation polytope. The diameter range conjecture. All integer numbers between $1$ and $p+q-1$, and only these, are realized as the diameters of $p \times q$ transportation polytopes.

This conjecture concerns the possible diameters of transportation-polytope graphs; its resolution status is not otherwise described in the supplied text.