Drawing 2-, 3- and 4-colorable Graphs in O(n²) Volume
Calamoneri, Tiziana and Sterbini, Andrea (1997) Drawing 2-, 3- and 4-colorable Graphs in O(n²) Volume. In: Symposium on Graph Drawing, GD '96, September 18-20, 1996, Berkeley, California, USA , pp. 53-62 (Official URL: http://dx.doi.org/10.1007/3-540-62495-3_37).
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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 leas1. t \Omega (n^(3/2)) 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.
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