Drawing 2-, 3- and 4-colorable graphs in O(n2) volume
A Fary grid drawing of a graph is a drawing on a three-dimensional grid such that vertices are placed at integer coordinates and edges are straight-lines such that no edge crossings are allowed.
In this paper it is proved that each k-colorable graph (k ≥ 2) needs at least Ω(n3/2)x volume to be drawn. Furthermore, it is shown how to draw 2-, 3- and 4-colorable graphs in a Fary grid fashion in O(n2) volume.
Keywordsk-colorable graphs Fary grid drawing 3D drawing
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