par Cabello, Sergio;Cardinal, Jean ;Langerman, Stefan
Référence Discrete & computational geometry, 50, 3, page (771-783)
Publication Publié, 2013-10
Article révisé par les pairs
Résumé : 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 (Comment Math Univ Carolinae 31(1):85-93, 1990). © 2013 Springer Science+Business Media New York.