Monotone Arc Diagrams with Few Biarcs
Year: 2024
Type: conference-paper
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.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891242122
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