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3D Visibility Representations of 1-planar Graphs

  • Patrizio Angelini
  • Michael A. Bekos
  • Michael Kaufmann
  • Fabrizio MontecchianiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)

Abstract

We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities between pairs of rectangles. In addition, the constructed representation is such that there is a plane that intersects all the rectangles, and this intersection defines a bar 1-visibility representation of G.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Michael A. Bekos
    • 1
  • Michael Kaufmann
    • 1
  • Fabrizio Montecchiani
    • 2
    Email author
  1. 1.Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Dipartimento di IngegneriaUniversitá degli Studi di PerugiaPerugiaItaly

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