AffiliationDepartment of Computer Science, University of Arizona
MetadataShow full item record
CitationGronemann, M., Hoffmann, M., Kobourov, S., & Schneck, T. Drawing Shortest Paths in Geodetic Graphs. In Graph Drawing and Network Visualization: 28th International Symposium, GD 2020, Vancouver, BC, Canada, September 16–18, 2020, Revised Selected Papers (p. 333). Springer Nature.
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Rights©Springer Nature Switzerland AG 2020
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractMotivated 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 G, i.e., an unweighted graph in which the shortest path between any pair of vertices is unique, is there a philogeodetic drawing of G, i.e., a drawing of G 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. © 2020, Springer Nature Switzerland AG.
Note12 month embargo; first published online 14 February 2021
VersionFinal accepted manuscript