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.
Cite
CITATION STYLE
Angelini, P., Bekos, M. A., Kaufmann, M., & Montecchiani, F. (2018). 3D visibility representations of 1-planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10692 LNCS, pp. 102–109). Springer Verlag. https://doi.org/10.1007/978-3-319-73915-1_9
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