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. %DIFDELCMD < {\bf %%% 770 (2019), 88--94] and  provide a 2-tree which does not allow any drawing with such bounded ratio . On the other hand, when the ratio is restricted to adjacent edges only, we provide a procedure that for any 2-tree yields a drawing with the ratio arbitrarily close to 4.
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. %DIFDELCMD < {\bf %%% 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.
A
, for any given constant r, we
R
allow any drawing with such bounded ratio . On the other hand, when the
admit a planar straight-line drawing with a ratio bounded by r. When the
R
provide a procedure that for
prove that
R
yields a drawing with the ratio arbitrarily close to
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