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 $m = O(D^{5/3} n^{1/3}\log^{4/3}n)$. In particular, every graph of bounded maximum degree can be drawn in a grid with volume $O(n \log^{4}n)$.

翻译：使用概率方法，我们获得了无交叉且具有低体积与小纵横比的图网格绘制。我们证明，每个包含$n$个顶点的$D$-退化图均可绘制在$[m]^3$中，其中$m = O(D^{5/3} n^{1/3}\log^{4/3}n)$。特别地，每个有界最大度图均可绘制在体积为$O(n \log^{4}n)$的网格中。