On the edge-length ratio of 2-trees
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We study planar straight-line drawings of graphs that minimize the ratio between the lenght of the longest and the shortest edge. We answer a question of Lazard et al. [Theor. Comput. Sci. 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.
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