Planar Projections of Graphs

Aravind, N. R. and Maniyar, Udit (2020) Planar Projections of Graphs. In: 6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020, 13-15 February 2020, Hyderabad.

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Abstract

We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on n vertices has a representation in \sqrt{n/2}+1 \rceil planes. In 3 dimensions, we show that there exist graphs with edges that can be projected onto two orthogonal planes, and that this is best possible. Finally, we obtain bounds in terms of parameters such as geometric thickness and linear arboricity. Using such a bound, we show that every graph of maximum degree 5 has a plane-projectable representation in 3 dimensions.

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