In this paper, we study the area requirements of planar straight-line orthogonal drawings of ternary trees. We prove that every ternary tree admits such a drawing in sub-quadratic area.

Further, we present upper bounds, the outcomes of an experimental evaluation, and a conjecture on the area requirements of planar straight-line orthogonal drawings of complete ternary trees.

Finally, we present a polynomial lower bound on the length of the minimum side of any planar straight-line orthogonal drawing of a complete ternary tree.

中文翻译：

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关于三叉树的平面直线正交图的面积要求

本文研究了三叉树的平面直线正交图的面积要求。我们证明每一个三叉树在次二次区域都接受这样的图形。

此外，我们提出了上限，实验评估的结果以及对完整三叉树的平面直线正交图的面积要求的猜想。

最后，我们给出了完整三叉树的任何平面直线正交图的最小边的长度的多项式下界。