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 $O(n \log n)$.

翻译：通过概率方法，我们获得了无交叉、低体积和较小纵横比的图网格绘制。我们证明了每个具有$n$个顶点的$D$-退化图都可以在$[m]^3$网格中绘制，其中$m^3 = O(D^2 n\log n)$。特别地，每个具有有界最大度数的图都可以在体积为$O(n \log n)$的网格中绘制。