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arXiv · 1709.00043

On the Edge-length Ratio of Outerplanar Graphs

Sylvain Lazard·William Lenhart·Giuseppe Liotta
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Abstract

We show that any outerplanar graph admits a planar straightline 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 $ε> 0$ there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than $2 - ε$. We also show that every bipartite outerplanar graph has a planar straight-line drawing with edge-length ratio 1, and that, for any $k \geq 1$, 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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Sylvain Lazard, William Lenhart, Giuseppe Liotta. 2017-08-31. On the Edge-length Ratio of Outerplanar Graphs. https://arxiv.org/abs/1709.00043

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