We study planar straight-line drawings of graphs that minimize the ratio between the length of the longest and the shortest edge. We answer a question of Lazard et al. [Theor. Comput. Sci. 770 (2019), 88--94] and, for any given constant $r$, we provide a $2$-tree which does not admit a planar straight-line drawing with a ratio bounded by $r$. When the ratio is restricted to adjacent edges only, we prove that any $2$-tree admits a planar straight-line drawing whose edge-length ratio is at most $4 + \varepsilon$ for any arbitrarily small $\varepsilon > 0$, hence the upper bound on the local edge-length ratio of partial $2$-trees is $4$.

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关于2-tree的边长比

我们研究图形的平面直线图，以最小化最长边和最短边的长度之间的比率。我们回答了 Lazard 等人的一个问题。[理论。计算。科学。770 (2019), 88--94] 并且，对于任何给定的常数 $r$，我们提供了一个 $2$-tree，它不允许绘制比例以 $r$ 为界的平面直线。当比率仅限于相邻边时，我们证明任何 $2$-tree 允许平面直线绘图，对于任何任意小的 $\varepsilon > 0$，边长比最多为 $4 + \varepsilon$，因此部分$2$-trees 的局部边长比的上限是$4$。