Planar graphs as L-intersection or L-contact graphs
Computational Geometry
2017-07-31 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1707.08833,
title = {Planar graphs as L-intersection or L-contact graphs},
author = {Daniel Gonçalves and Lucas Isenmann and Claire Pennarun},
journal= {arXiv preprint arXiv:1707.08833},
year = {2017}
}