The Clique Problem in Ray Intersection Graphs
Computational Geometry
2011-11-28 v1 Computational Complexity
Abstract
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and implies that finding a maximum clique in a segment intersection graph is NP-hard. This solves a 21-year old open problem posed by Kratochv\'il and Ne\v{s}et\v{r}il.
Cite
@article{arxiv.1111.5986,
title = {The Clique Problem in Ray Intersection Graphs},
author = {Sergio Cabello and Jean Cardinal and Stefan Langerman},
journal= {arXiv preprint arXiv:1111.5986},
year = {2011}
}
Comments
12 pages, 7 figures