3D Visibility Representations of 1-planar Graphs

Angelini, Patrizio and Bekos, Michael A. and Kaufmann, Michael and Montecchiani, Fabrizio (2017) 3D Visibility Representations of 1-planar Graphs. In: Graph Drawing and Network Visualization, GD 2017, September 25-27 , pp. 102-109(Official URL: https://doi.org/10.1007/978-3-319-73915-1_9).

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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.

Item Type: Conference Paper
Classifications: P Styles > P.060 3D
P Styles > P.900 Visibility
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1593

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