Monotone Arc Diagrams with Few Biarcs

Steven Chaplick*, Henry Förster*, Michael Hoffmann*, Michael Kaufmann*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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 languageEnglish
Title of host publication32nd International Symposium on Graph Drawing and Network Visualization, GD 2024
EditorsStefan Felsner, Karsten Klein
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume320
ISBN (Electronic)9783959773430
DOIs
Publication statusPublished - 28 Oct 2024
Event32nd International Symposium on Graph Drawing and Network Visualization, GD 2024 - Vienna, Austria
Duration: 18 Sept 202420 Sept 2024
Conference number: 32nd

Publication series

SeriesLeibniz International Proceedings in Informatics, LIPIcs
Number11
Volume320
ISSN1868-8969

Conference

Conference32nd International Symposium on Graph Drawing and Network Visualization, GD 2024
Country/TerritoryAustria
CityVienna
Period18/09/2420/09/24

Keywords

  • linear layout
  • monotone drawing
  • planar graph
  • topological book embedding

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