All Questions

Suppose $G$ is a graph embedded in the plane with $m=|E(G)|$ edges and $n=|V(G)|$ vertices. Suppose $\operatorname{sim}(G)$, the simplification of $G$ contains $ m' \gg 3n $ edges. Call the set of ...

Let $T$ be a given (finite) tree. Question 1: Is it always possible to add edges to $T$ to obtain a $2$-connected outerplanar supergraph $G$? Question 2: If the answer to Question #1 is negative, can ...