Some Results On Point Visibility Graphs

TL;DR

This paper advances understanding of point visibility graphs by establishing recognition conditions, analyzing their computational complexity, and providing a complete characterization for planar cases enabling efficient algorithms.

Contribution

It introduces three necessary conditions for recognizing point visibility graphs and offers a complete characterization for planar graphs with a linear time recognition algorithm.

Findings

Recognition problem is in PSPACE.

Complete characterization for planar point visibility graphs.

Linear time recognition and reconstruction algorithm for planar cases.

Abstract

In this paper, we present three necessary conditions for recognizing point visibility graphs. We show that this recognition problem lies in PSPACE. We state new properties of point visibility graphs along with some known properties that are important in understanding point visibility graphs. For planar point visibility graphs, we present a complete characterization which leads to a linear time recognition and reconstruction algorithm.