All Questions

Let $G$ be a plane $3$-connected graph; so it partitions the plane into regions bounded by faces. Let $\mathrm{deg}_v$ be the sequence of vertex degrees of $G$, and $\mathrm{deg}_f$ be the sequence of ...

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 ...

Test Polygon: Consider the following polygon as attached. Let the known parameter be as follows: •Member to member connectivity, i.e. it is known that A – B, X – E, F – B, etc. for all the members. •...