Planar graphs as L-intersection or L-contact graphs

@inproceedings{Gonalves2018PlanarGA,
  title={Planar graphs as L-intersection or L-contact graphs},
  author={Daniel Gonçalves and Lucas Isenmann and Claire Pennarun},
  booktitle={SODA},
  year={2018}
}
The x-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel x shapes in the plane. A subfamily of these graphs are {x, |,−}-contact graphs which are the contact graphs of axis parallel x, |, 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 x-intersection graphs, and that triangle-free planar graphs are {x, |,−}-contact graphs. These results are obtained by a… CONTINUE READING
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