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Segment representation of a subclass of co-planar graphs

Mathew C. Francis 1 Jan Kratochvil 2 Tomáš Vyskočil 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A graph is a segment graph if its vertices can be mapped to line segments in the plane such that two vertices are adjacent if and only if their corresponding line segments intersect. Kratochvíl and Kuběna asked the question of whether the complements of planar graphs, called co-planar graphs, are segment graphs. We show here that the complements of all partial 2-trees are segment graphs.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00807948
Contributor : Daniel Gonçalves <>
Submitted on : Thursday, April 4, 2013 - 4:09:45 PM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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Mathew C. Francis, Jan Kratochvil, Tomáš Vyskočil. Segment representation of a subclass of co-planar graphs. Discrete Mathematics, Elsevier, 2012, 312, pp.1815-1818. ⟨lirmm-00807948⟩

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