All Questions

By "roundest" I mean having the lowest surface area for the highest volume, given a fixed number of faces $n$. There've been a few questions about them on here (including from me), but I'm ...

Given the complete graph $K_n=(V,E)$, the Traveling Salesman Polytope is a convex polytope in $\Bbb R^E$ obtained as the convex hull of the indicator vectors of (edge-sets of) Hamiltonian cycles in $...

Let $Q \subseteq R^n$ be a rational polyhedron and let $Q_I=Convexhull(Q \cap Z^n)$. By finite basis theorem, we have $Q=P+C$ for some rational polytope $P$ and finitely generated cone $C$ where $C=R_+...

Are there any papers/textbooks/monographs that describe distinguishing properties of the polytopes that arise when solving the linear relaxation of well-known integer programs? For example, it is ...

It is well known, that the optimal tours are invariant under the addition of vertex weights; it is also known, that minimum spanning trees provide an upper bound on the length of the shortest Hamilton ...

Let $P$ and $V$ be, respectively, a bounded full-dimensional polytope and an $m$-dimensional affine subspace of $\mathbb R^n$, and assume $P \cap V$ is non-empty. Q1. Could you provide me with a ...