Plane Multigraphs with One-Bend and Circular-Arc Edges of a Fixed Angle
March 2024
Pages 15 - 31
Abstract
For an angle, we consider plane graphs and multigraphs in which the edges are either (i) one-bend polylines with an angle between the two edge segments, or (ii) circular arcs of central angle . We derive upper and lower bounds on the maximum density of such graphs in terms of . As an application, we improve upon bounds for the number of edges in graphs (i.e., graphs that can be drawn in the plane with one-bend edges such that any two crossing edges meet at angle ). This is the first improvement on the size of graphs in over a decade.
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Published In
Mar 2024
448 pages
ISBN:978-981-97-0565-8
DOI:10.1007/978-981-97-0566-5
- Editors:
- Ryuhei Uehara,
- Katsuhisa Yamanaka,
- Hsu-Chun Yen
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 18 March 2024
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