On the EdgeLength Ratio of Outerplanar GraphsLazard, Sylvain and Lenhart, Wiliam J. and Liotta, Giuseppe (2017) On the EdgeLength Ratio of Outerplanar Graphs. In: Graph Drawing and Network Visualization. GD 2017, September 2527 , pp. 1723(Official URL: https://doi.org/10.1007/9783319739151_2). Full text not available from this repository.
Official URL: https://doi.org/10.1007/9783319739151_2
AbstractWe 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 edgelength ratio smaller than 2−ϵ. We also show that every bipartite outerplanar graph has a planar straightline drawing with edgelength ratio 1, and that, for any k≥1, there exists an outerplanar graph with a given combinatorial embedding such that any planar straightline drawing has edgelength ratio greater than k.
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