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Drawing 2-, 3- and 4-colorable graphs in O(n2) volume

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (1997) 1190 53-62
DOI: 10.1007/3-540-62495-3_37
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Abstract

A Fary grid drawing of a graph is a drawing on a threedimensional 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) 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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Calamoneri, T., & Sterbini, A. (1997). Drawing 2-, 3- and 4-colorable graphs in O(n2) volume. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1190, pp. 53–62). Springer Verlag. https://doi.org/10.1007/3-540-62495-3_37

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