3 problems

Maximum partial-dual genus conjecture. If $G\not\cong C_3$ is a $\lambda$-edge-connected planar graph with $\lambda\in\{1,2\}$, then

A ribbon graph is orientable if its underlying surface is orientable, and its partial-dual genus polynomial records the genera of all partial duals. A polynomial is non-constant if…

Let $G$ be a non-orientable ribbon graph. Its partial-dual Euler-genus polynomial is the generating function … where $G^A$ is the partial dual of $G$ with respect to…