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.File in questo prodotto:
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