8 problems

Let $k$ and $n$ be positive integers with $n=2k$. For a bipartite $(k,2k)$-plabic graph $G$, let $G^{\operatorname{op}}$ be the graph obtained from $G$ by a $180^\circ$ rotation fo…

Hirsch-sharpness conjecture for 3-way transportation polytopes.

Hyperplane Diameter Conjecture.

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

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…