All Questions

It is a notorious open problem to find a smallest set of $N$ points that permit any $n$-vertex planar graph to be drawn in the plane without crossings, using only those $N$ points as vertices, and ...

I would like to see Cayley graphs drawn in 3-dimensional Euclidean space such that the vertices are represented by points and various shadows display the actions of the generators. For example, ...

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 ...

So in terms of crossing number https://arxiv.org/pdf/1808.10480 gives a lower bound of $O(e^{2.5}/n^{1.5})$ for multigraphs with no face of length 2 with no node contained inside. What do we know ...

Let $G$ be a graph embedded in the plane (with crossings). For $ F \subset E(G) $, denote by $c(F)$ the set of edges of $G$ that cross some edge in $F$. Denote $\delta(v)$ the set of edges with one ...

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 ...