2017/08/31 by Lazard, Sylvain, Lenhart, William, Liotta, Giuseppe
#Computational Geometry (cs.CG) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1709.00043
We 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 edge-length ratio smaller than 2 - ε. We also show that every bipartite outerplanar graph has a planar straight-line drawing with edge-length ratio 1, and that, for any k ≥ 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.