3-Colorable Planar Graphs Have an Intersection Segment Representation Using 3 Slopes - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Conference Papers Year : 2019

3-Colorable Planar Graphs Have an Intersection Segment Representation Using 3 Slopes

Abstract

In his PhD Thesis E.R. Scheinerman conjectured that planar graphs are intersection graphs of segments in the plane. This conjecture was proved with two different approaches. In the case of 3-colorable planar graphs E.R. Scheinerman conjectured that it is possible to restrict the set of slopes used by the segments to only 3 slopes. Here we prove this conjecture by using an approach introduced by S. Felsner to deal with contact representations of planar graphs with homothetic triangles.
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Dates and versions

lirmm-02407838 , version 1 (13-12-2019)

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Daniel Gonçalves. 3-Colorable Planar Graphs Have an Intersection Segment Representation Using 3 Slopes. WG 2019 - 45th International Workshop on Graph-Theoretic Concepts in Computer Science, Jun 2019, Vall de Núria, Spain. pp.351-363, ⟨10.1007/978-3-030-30786-8_27⟩. ⟨lirmm-02407838⟩
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