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 vf into each face f of T and then connecting vf to the three vertices of f.
Original language | English |
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Title of host publication | 32nd International Symposium on Graph Drawing and Network Visualization, GD 2024 |
Editors | Stefan Felsner, Karsten Klein |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Volume | 320 |
ISBN (Electronic) | 9783959773430 |
DOIs | |
Publication status | Published - 28 Oct 2024 |
Event | 32nd International Symposium on Graph Drawing and Network Visualization, GD 2024 - Vienna, Austria Duration: 18 Sept 2024 → 20 Sept 2024 Conference number: 32nd |
Publication series
Series | Leibniz International Proceedings in Informatics, LIPIcs |
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Number | 11 |
Volume | 320 |
ISSN | 1868-8969 |
Conference
Conference | 32nd International Symposium on Graph Drawing and Network Visualization, GD 2024 |
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Country/Territory | Austria |
City | Vienna |
Period | 18/09/24 → 20/09/24 |
Keywords
- linear layout
- monotone drawing
- planar graph
- topological book embedding