5 problems

Let $P$ be a polytope, with a vertex/edge graph whose diameter is measured in graph distance. The Polynomial Hirsch Conjecture is a central problem of Discrete Geometry, stating th…

Borradaile et al.'s conjecture. A strong orientation of $G$ is decreasingly minimal among strong orientations if and only if there is no small improvement preserving strong connect…

Let $\Delta_{k,q}$ be the set of integer vectors in $\mathbb{Z}^k$ with non-negative entries summing to $q$, and consider a Sperner-admissible labeling of a regular simplicial subd…

Complexity-hierarchy conjecture. The two-stage setting proposed here with a variant of two-stage discrete uncertainty moves up one level in the complexity hierarchy, and problems b…

Referee's uniqueness conjecture. If $g_i$ is defined without rounding, then there is a unique persistent labeling.