English

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.

Keywords

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

R2 v1 2026-06-21T19:41:32.313Z