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Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every D-degenerate graph on n vertices can be drawn in [m]³ where m = O(D5/3 n1/3log4/3n). In particular, every graph of bounded maximum degree can be drawn in a grid with volume O(n log⁴n).
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Balogh et al. (2024) studied this question.
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