2 problems

Let $G$ be a planar graph and let $(H,f)$ be a positive-valued cover, meaning that the cover function $f$ is positive-valued. Let $\kappa\geq 2$. A strictly $f$-degenerate transver…

Let $G$ be a toroidal graph with no subgraph isomorphic to any configuration in the family denoted by $E$. Let $(H,f)$ be a cover of $G$, where $f$ assigns to each vertex of $H$ a…