The Clique Problem in Ray Intersection Graphs
Sergio Cabello, Jean Cardinal, Stefan Langerman · arXiv (Cornell University) · 2011
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 Kratochvíl and Nešetřil.