Planar graphs as L-intersection or L-contact graphs

Daniel Gonçalves 1 Lucas Isenmann 1 Claire Pennarun 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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.
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https://hal.archives-ouvertes.fr/hal-01569535
Contributor : Claire Pennarun <>
Submitted on : Friday, July 28, 2017 - 4:24:03 AM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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  • HAL Id : hal-01569535, version 2
  • ARXIV : 1707.08833

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

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