When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

Two points in a polygon are called if the straight line between them lies entirely inside the
polygon. The art gallery problem for a polygon P is to find a minimum set of points G in P …

A human observer can effortlessly identify visible portions of geometric objects present in the
environment. However, computations of visible portions of objects from a viewpoint involving …

Unsolved problems in visibility graphs of points, segments, and polygons Page 1 22 Unsolved
Problems in Visibility Graphs of Points, Segments, and Polygons SUBIR K. GHOSH, Tata …

A point visibility graph is a graph induced by a set of points in the plane, where every vertex
corresponds to a point, and two vertices are adjacent whenever the two corresponding …

In this paper we establish four necessary conditions for recognizing visibility graphs of
simple polygons and conjecture that these conditions are sufficient. We present an 0 (n 2) …

The recognition problem for visibility graphs is, given a graph, to determine whether it is the
visibility graph of a simple polygon. The complexity of this problem is unknown. In this paper …

A new necessary condition for a graph G to be the visibility graph of a simple polygon is
given: each 3-connected component of G must. have a vertex ordering in which every vertex …

Computational geometry column 18 Page 1 Computational Geometry Column 1 8 Joseph O'Rourke
* Abstract Results on visibility graphs are classified and organized into five tables . 1 …

The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor
is it known to be NP-hard. It is, however, known to be in PSPACE. Further, every such …