The Clique Problem in Ray Intersection Graphs

Details The Clique Problem in Ray Intersection Graphs The Clique Problem in Ray Intersection Graphs

2011-11-25

arxiv.org/abs/1111.5986v1

Computer Science

Computational Geometry

12 pages, 7 figures

Scientific paper

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.

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