4 problems

Continuous analogue of the Hirsch conjecture. The total curvature of the central path is linearly bounded in the number of constraints.

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 $F_N$ be the new facet in a translation sequence of a polytope, and let $x,y$ be the vertices defining the paths under consideration. Contiguous-path conjecture. Every edge adj…

Let $P$ be a $(d,2d-1)$-polytope with graph $G_P$, and let $x,y$ be vertices of $P$. A collection of $(x,y)$ paths spans the graph if removing one vertex from every path disconnect…