# On the Edge-length Ratio of Outerplanar Graphs

1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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 $k \geq 1$, 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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Conference papers

Cited literature [13 references]

https://hal.inria.fr/hal-01591699
Contributor : Sylvain Lazard <>
Submitted on : Thursday, September 21, 2017 - 6:29:47 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:26 PM

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• HAL Id : hal-01591699, version 1

### Citation

Sylvain Lazard, William Lenhart, Giuseppe Liotta. On the Edge-length Ratio of Outerplanar Graphs. International Symposium on Graph Drawing and Network Visualization, 2017, Boston, United States. ⟨hal-01591699⟩

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