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arXiv · 1708.06196

3D Visibility Representations of 1-planar Graphs

Patrizio Angelini·Michael A. Bekos·Michael Kaufmann·Fabrizio Montecchiani
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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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Patrizio Angelini, Michael A. Bekos, Michael Kaufmann, Fabrizio Montecchiani. 2017-08-21. 3D Visibility Representations of 1-planar Graphs. https://arxiv.org/abs/1708.06196

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