# curvature

## Continous analogue of Hirsch conjecture ★★

Author(s): Deza; Terlaky; Zinchenko

\begin{conjecture} The order of the largest total curvature of the primal central path over all polytopes defined by $n$ inequalities in dimension $d$ is $n$. \end{conjecture}

## What is the largest graph of positive curvature? ★

\begin{problem} What is the largest connected \Def{planar graph} of minimum degree 3 which has everywhere positive combinatorial curvature, but is not a \Def[prism]{prism (geometry)} or \Def{antiprism}? \end{problem}

Keywords: curvature; planar graph