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    Drawing Shortest Paths in Geodetic Graphs

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    Author
    Cornelsen, Sabine
    Pfister, Maximilian
    Förster, Henry
    Gronemann, Martin
    Hoffmann, Michael
    Kobourov, Stephen
    Schneck, Thomas
    Affiliation
    Department of Computer Science, University of Arizona
    Issue Date
    2021-02-14
    Keywords
    Edge crossings
    Geodetic graphs
    Unique shortest paths
    
    Metadata
    Show full item record
    Publisher
    Springer Science and Business Media Deutschland GmbH
    Citation
    Gronemann, 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.
    Journal
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Rights
    ©Springer Nature Switzerland AG 2020.
    Collection Information
    This 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 repository@u.library.arizona.edu.
    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 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.
    Note
    12 month embargo; first published online 14 February 2021
    ISSN
    0302-9743
    EISSN
    1611-3349
    DOI
    10.1007/978-3-030-68766-3_26
    Version
    Final accepted manuscript
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-030-68766-3_26
    Scopus Count
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    UA Faculty Publications

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