Planar graphs as L-intersection or L-contact graphs

Daniel Gonçalves (1) , Lucas Isenmann (1) , Claire Pennarun (2)

1 ALGCO - Algorithmes, Graphes et Combinatoire
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The L-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel shapes in the plane. A subfamily of these graphs are {L, |, −}-contact graphs which are the contact graphs of axis parallel L, |, and − shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are L-intersection graphs, and that triangle-free planar graphs are {L, |, −}-contact graphs. These results are obtained by a new and simple decomposition technique for 4-connected triangulations. Our results also provide a much simpler proof of the known fact that planar graphs are segment intersection graphs.

Domaines: Géométrie algorithmique [cs.CG]

Daniel Gonçalves, Lucas Isenmann, Claire Pennarun. Planar graphs as L-intersection or L-contact graphs. 2017. ⟨hal-01569535v2⟩