Drawing Shortest Paths in Geodetic Graphs

Sabine Cornelsen, Maximilian Pfister, Henry Förster, Martin Gronemann, Michael Hoffmann, Stephen Kobourov, Thomas Schneck

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationGraph Drawing and Network Visualization - 28th International Symposium, GD 2020, Revised Selected Papers
EditorsDavid Auber, Pavel Valtr
PublisherSpringer Science and Business Media Deutschland GmbH
Pages333-340
Number of pages8
ISBN (Print)9783030687656
DOIs
StatePublished - 2020
Event28th International Symposium on Graph Drawing and Network Visualization, GD 2020 - Virtual, Online
Duration: Sep 16 2020Sep 18 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12590 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference28th International Symposium on Graph Drawing and Network Visualization, GD 2020
CityVirtual, Online
Period9/16/209/18/20

Keywords

  • Edge crossings
  • Geodetic graphs
  • Unique shortest paths

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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