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Two-Planar Graphs Are Quasiplanar

Authors Michael Hoffmann, Csaba D. Tóth

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Michael Hoffmann
Csaba D. Tóth

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Michael Hoffmann and Csaba D. Tóth. Two-Planar Graphs Are Quasiplanar. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.MFCS.2017.47

Abstract

It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further show that quasiplanarity is witnessed by a simple topological drawing, that is, any two edges cross at most once and adjacent edges do not cross.

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Keywords
  • graph drawing
  • near-planar graph
  • simple topological plane graph

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