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 ...

Given a nonplanar graph $G$ drawn in the plane with crossings. Does there exist a small ($o(|V(G)|$) subset $S$ of edges of $G$ such that after the removal of all edges that intersect or share an ...