On the Planar Edge-Length Ratio of Planar Graphs
Data Structures and Algorithms
2020-04-14 v3 Computational Geometry
Combinatorics
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 -vertex planar graphs whose planar edge-length ratio is in ; 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.
Keywords
Cite
@article{arxiv.1908.03586,
title = {On the Planar Edge-Length Ratio of Planar Graphs},
author = {Manuel Borrazzo and Fabrizio Frati},
journal= {arXiv preprint arXiv:1908.03586},
year = {2020}
}
Comments
Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)