6 problems

Let $N_1$ and $N_2$ be positive integers, and consider $N_1\times N_2$ transportation polytopes and their graph diameters. Diameter-realisation conjecture. All integers between $1$…

Let a $p \times q \times s$ generalized central transportation polytope be the $3$-way transportation polytope whose $2$-margins are the $q \times s$ matrix $U$ with entries…

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 $p+q-1$…

Let $p \times q \times s$ be a non-degenerate $3$-way transportation polytope specified by $2$-margin matrices $U,V,W$, and let $f_0(M(U,V,W))$ denote its number of vertices. The g…

Hirsch-sharpness conjecture for 3-way transportation polytopes.

Let $P_c=\{x\mid Bx=c,\ x\geq 0\}$ be a non-degenerate $m\times n$ classical transportation polytope, and let its graph have the vertices and edges of $P_c$. Hamiltonian-cycle conj…