Computational complexity aspects of point visibility graphs

Algorithmic Aspects of Point Visibility Graphs

A point visibility graph is a graph induced by a set of points in the plane where the vertices of the graph represent the points in the point set and two vertices are adjacent if and only if no other point from the point set lies on the line segment between the two corresponding points. The set of all point visibility graphs form a graph class which is examined from a computational complexity p...

Recognition and Complexity of Point Visibility Graphs

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 points are visible from each other, that is, the open segment between them does not contain any other point of the set. We study the recognition problem for point visibility graphs: given a simple undirected graph, d...

On Colouring Point Visibility Graphs

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromat...

Computational Complexity of Graphs

Complexity is one of the crucial scientific phenomena of our times. There are many possible ways tomeasure the “complexity” of a given finite object taken from a known underlying set of objects. In the information-theoretic sense, an object is treated as “complex”, if many binary bits are necessary to encode the object, that is, many bits are necessary to distinguish it from the remaining objec...

On Rectangle Visibility Graphs. III. External Visibility and Complexity