5 problems

Let $P$ be an even simple $3$-polytope, meaning that every facet of $P$ has an even number of vertices. Its vertex-edge graph is the graph whose vertices and edges are those of $P$…

Let $P$ range over all $3$-dimensional polytopes with $n$ vertices, and let $f$ range over all generic linear functionals on $P$. Write $G(P,f)$ for the flip graph associated with…

Let $P$ be a simple $3$-dimensional polytope with $2n$ vertices, and let $f$ be a generic linear functional on $P$. Let $\b5(P,f)$ denote the number of $f$-monotone paths on $P$, a…

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…