LIPIcs.GD.2024.11.pdf
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Monotone Arc Diagrams with Few Biarcs
Authors
Steven Chaplick 
,
Henry Förster ,
Michael Hoffmann ,
Michael Kaufmann
-
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Volume:
32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Graph Drawing and Network Visualization (GD) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-10-28
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Acknowledgements
This work started at the workshop on Graph and Network Visualization (GNV 2017) in Heiligkreuztal, Germany. Preliminary results were presented at the 36th European Workshop on Computational Geometry (EuroCG 2020). We thank Stefan Felsner and Stephen Kobourov for useful discussions.
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Steven Chaplick, Henry Förster, Michael Hoffmann, and Michael Kaufmann. Monotone Arc Diagrams with Few Biarcs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.11
Abstract
We show that every planar graph has a monotone topological 2-page book embedding where at most (4n-10)/5 (of potentially 3n-6) edges cross the spine, and every edge crosses the spine at most once; such an edge is called a biarc. We can also guarantee that all edges that cross the spine cross it in the same direction (e.g., from bottom to top). For planar 3-trees we can further improve the bound to (3n-9)/4, and for so-called Kleetopes we obtain a bound of at most (n-8)/3 edges that cross the spine. The bound for Kleetopes is tight, even if the drawing is not required to be monotone. A Kleetope is a plane triangulation that is derived from another plane triangulation T by inserting a new vertex v_f into each face f of T and then connecting v_f to the three vertices of f.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Combinatorics
- Mathematics of computing → Graph theory
- Human-centered computing → Graph drawings
Keywords
- planar graph
- topological book embedding
- monotone drawing
- linear layout
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References
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