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 ϵ>0 there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than 2−ϵ. We also show that this ratio cannot be bounded if the embeddings of the outerplanar graphs are given.

On the edge-length ratio of outerplanar graphs

Liotta G.
2019

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 ϵ>0 there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than 2−ϵ. We also show that this ratio cannot be bounded if the embeddings of the outerplanar graphs are given.
2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1460838
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