3 problems

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…

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…