8 problems

Let $P$ be a polytope. A path $P'$ in its graph is nonrevisiting if, for every facet of the polytope, the intersection of $P'$ with that facet is either empty or a path in the face…

Non-revisiting Conjecture. There is a path from $u$ to $v$ which at every step enters a different facet of $P$.

Hirsch-sharpness conjecture for 3-way transportation polytopes.

Hyperplane Diameter Conjecture.

The $d$-step Conjecture. For every $d \geq 2$,

Polynomial Diameter Conjecture. Is there a polynomial function $f(n,d)$ such that

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…