5 problems

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 $P$ be a non-degenerate $l\times m\times n$ axial transportation polytope with $l,m,n\geq 3$. Its dimension is … Let $f$ be the number of facets of $P$, and let $G(P)$ be its g…

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…