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The Clique Problem in Ray Intersection Graphs (1111.5986v1)
Published 25 Nov 2011 in cs.CG and cs.CC
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.