# 3-Connected Planar Graphs

## On Planar Greedy Drawings of 3-Connected Planar Graphs

A graph drawing is greedy if, for every ordered pair of vertices $(x,y)$, there is a path from $x$ to $y$ such that the Euclidean distance to $y$ decreases monotonically at every vertex of the path. Greedy drawings support a simple geometric routing …

## Reaching 3-Connectivity via Edge-edge Additions

Given a graph $G$ and a pair $\langle e',e''\rangle$ of distinct edges of $G$, an edge-edge addition on $\langle e',e''\rangle$ is an operation that turns $G$ into a new graph $G'$ by subdividing edges $e'$ and $e''$ with a dummy vertex $v'$ and …

## Drawing Planar Graphs with Many Collinear Vertices

Consider the following problem$:$ Given a planar graph $G$, what is the maximum number $p$ such that $G$ has a planar straight-line drawing with $p$ collinear vertices? This problem resides at the core of several graph drawing problems, including …

## On Planar Greedy Drawings of 3-Connected Planar Graphs

A graph drawing is greedy if, for every ordered pair of vertices $(x,y)$, there is a path from $x$ to $y$ such that the Euclidean distance to $y$ decreases monotonically at every vertex of the path. Greedy drawings support a simple geometric routing …

## Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs

A square-contact representation of a planar graph $G=(V,E)$ maps the vertices in $V$ to interior disjoint axis-aligned squares in the plane and the edges in $E$ to adjacencies between the sides of the squares corresponding to the endpoints of each …

## Drawing Planar Graphs with Many Collinear Vertices

Consider the following problem$:$ Given a planar graph $G$, what is the maximum number $p$ such that $G$ has a planar straight-line drawing with $p$ collinear vertices? This problem resides at the core of several graph drawing problems, including …