Drawing Shortest Paths in Geodetic Graphs
Abstract
Motivated by the fact that in a space where shortest paths are unique, no two shortest paths meet twice, we study a question posed by Greg Bodwin: Given a geodetic graph , i.e., an unweighted graph in which the shortest path between any pair of vertices is unique, is there a philogeodetic drawing of , i.e., a drawing of in which the curves of any two shortest paths meet at most once? We answer this question in the negative by showing the existence of geodetic graphs that require some pair of shortest paths to cross at least four times. The bound on the number of crossings is tight for the class of graphs we construct. Furthermore, we exhibit geodetic graphs of diameter two that do not admit a philogeodetic drawing.
Cite
@article{arxiv.2008.07637,
title = {Drawing Shortest Paths in Geodetic Graphs},
author = {Sabine Cornelsen and Maximilian Pfister and Henry Förster and Martin Gronemann and Michael Hoffmann and Stephen Kobourov and Thomas Schneck},
journal= {arXiv preprint arXiv:2008.07637},
year = {2020}
}
Comments
Appears in the Proceedings of the 28th International Symposium on Graph Drawing and Network Visualization (GD 2020)