3D Visibility Representations of 1-planar Graphs
Computational Geometry
2017-08-22 v1
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.
Keywords
Cite
@article{arxiv.1708.06196,
title = {3D Visibility Representations of 1-planar Graphs},
author = {Patrizio Angelini and Michael A. Bekos and Michael Kaufmann and Fabrizio Montecchiani},
journal= {arXiv preprint arXiv:1708.06196},
year = {2017}
}
Comments
Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017)