TY - GEN
T1 - Drawing Shortest Paths in Geodetic Graphs
AU - Cornelsen, Sabine
AU - Pfister, Maximilian
AU - Förster, Henry
AU - Gronemann, Martin
AU - Hoffmann, Michael
AU - Kobourov, Stephen
AU - Schneck, Thomas
N1 - Funding Information:
This research began at the Graph and Network Visualization Workshop 2019 (GNV’19) in Heiligkreuztal. S. C. is funded by the German Research Foundation DFG – Project-ID 50974019 – TRR 161 (B06). M. H. is supported by the Swiss National Science Foundation within the collaborative DACH project Arrangements and Drawings as SNSF Project 200021E-171681. S. K. is supported by NSF grants CCF-1740858, CCF-1712119, and DMS-1839274.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Edge crossings
KW - Geodetic graphs
KW - Unique shortest paths
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U2 - 10.1007/978-3-030-68766-3_26
DO - 10.1007/978-3-030-68766-3_26
M3 - Conference contribution
AN - SCOPUS:85102745745
SN - 9783030687656
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 333
EP - 340
BT - Graph Drawing and Network Visualization - 28th International Symposium, GD 2020, Revised Selected Papers
A2 - Auber, David
A2 - Valtr, Pavel
PB - Springer Science and Business Media Deutschland GmbH
T2 - 28th International Symposium on Graph Drawing and Network Visualization, GD 2020
Y2 - 16 September 2020 through 18 September 2020
ER -