Some Results On Point Visibility Graphs
  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. 
Subir Kumar Ghosh and Bodhayan Roy
cs.CG cs.DM math.CO