Grid-drawings of graphs in three-dimensions
<|reference_start|>Grid-drawings of graphs in three-dimensions: 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 $m^3 = O(D^2 n\log n)$. In particular, every graph of bounded maximum degree can be drawn in a grid with volume $O(n \log n)$.<|reference_end|>
@article{balogh2024grid-drawings,
    title={Grid-drawings of graphs in three-dimensions},
    author={Jozsef Balogh, Ethan Patrick White},
    journal={arXiv preprint arXiv:2404.02369},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.02369},
    primaryClass={math.CO cs.DM}
}