A Characterization of Visibility Graphs for Pseudo-Polygons

TL;DR

This paper characterizes the visibility graphs of pseudo-polygons by identifying key properties and necessary conditions, proving their sufficiency through a reduction to existing vertex-edge visibility graph characterizations.

Contribution

It provides a complete characterization of pseudo-polygon visibility graphs by establishing necessary and sufficient conditions based on combinatorial properties.

Findings

Five necessary conditions for pseudo-polygon visibility graphs

Proof that these conditions are also sufficient

Reduction to known vertex-edge visibility graph characterization

Abstract

In this paper, we give a characterization of the visibility graphs of pseudo-polygons. We first identify some key combinatorial properties of pseudo-polygons, and we then give a set of five necessary conditions based off our identified properties. We then prove that these necessary conditions are also sufficient via a reduction to a characterization of vertex-edge visibility graphs given by O'Rourke and Streinu.