# Minimal Representations of Order Types by Geometric Graphs

## TL;DR

This paper introduces a new concept called exit edges to create minimal geometric graphs that preserve the order type of a point set, enabling compact and unambiguous visualizations.

## Contribution

It defines exit edges, provides methods to compute them efficiently, and establishes bounds on their number for minimal order type representations.

## Key findings

- Exit edges prevent order type changes under vertex motion.
- Efficient algorithms for computing exit edges.
- Bounds established on the number of exit edges.

## Abstract

In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices. That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.