Every Planar Graph is the Intersection Graph of Segments in the Plane: Extended Abstract

Jérémie Chalopin (1) , Daniel Gonçalves (2)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
2 ALGCO - Algorithmes, Graphes et Combinatoire

Given a set S of segments in the plane, the intersection graph of S is the graph with vertex set S in which two vertices are adjacent if and only if the corresponding two segments intersect. We prove a conjecture of Scheinerman (PhD Thesis, Princeton\nUniversity, 1984) that every planar graph is the intersection graph of some segments in the plane.

Mots clés: intersection graphs; planar graphs

Domaines: Combinatoire [math.CO]

Jérémie Chalopin, Daniel Gonçalves. Every Planar Graph is the Intersection Graph of Segments in the Plane: Extended Abstract. STOC '09: 41st ACM Symposium on Theory of Computing, May 2009, France. pp.631-638. ⟨lirmm-00395364⟩