1. Computational complexity aspects of point visibility graphs
- Author
-
Pascal Kunz, Anne-Sophie Himmel, Clemens Hoffmann, Vincent Froese, and Manuel Sorge
- Subjects
Induced path ,Computational complexity theory ,Applied Mathematics ,Visibility graph ,0211 other engineering and technologies ,021107 urban & regional planning ,0102 computer and information sciences ,02 engineering and technology ,Grid ,01 natural sciences ,Combinatorics ,Line segment ,010201 computation theory & mathematics ,If and only if ,Dominating set ,Discrete Mathematics and Combinatorics ,Feedback vertex set ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics - Abstract
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 perspective in this paper. We show NP-hardness for several classic graph problems on point visibility graphs such as Feedback Vertex Set , Longest Induced Path , Bisection and F - Free Vertex Deletion (for certain sets F ). Furthermore, we consider the complexity of the Dominating Set problem on point visibility graphs of points on a grid.
- Published
- 2019
- Full Text
- View/download PDF