Abstract
We show that any outerplanar graph admits a planar straight-line drawing such that the length ratio of the longest to the shortest edges is strictly less than 2. This result is tight in the sense that for any \(\epsilon > 0\) there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than \(2 - \epsilon \). We also show that every bipartite outerplanar graph has a planar straight-line drawing with edge-length ratio 1, and that, for any \(k \ge 1\), there exists an outerplanar graph with a given combinatorial embedding such that any planar straight-line drawing has edge-length ratio greater than k.
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