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arXiv · 1908.03586

On the Planar Edge-Length Ratio of Planar Graphs

Manuel Borrazzo·Fabrizio Frati
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Abstract

The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight-line drawing of the graph. In this paper, we study the planar edge-length ratio of planar graphs. We prove that there exist $n$-vertex planar graphs whose planar edge-length ratio is in $\Omega(n)$; this bound is tight. We also prove upper bounds on the planar edge-length ratio of several families of planar graphs, including series-parallel graphs and bipartite planar graphs.

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Manuel Borrazzo, Fabrizio Frati. 2019-08-09. On the Planar Edge-Length Ratio of Planar Graphs. https://arxiv.org/abs/1908.03586

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