On Optimal Beyond-Planar Graphs

Authors

  • Franz Brandenburg University of Passau (emeritus)

DOI:

https://doi.org/10.57717/cgt.v2i1.10

Abstract

A graph is  beyond-planar if it can be drawn in the plane with a specific restriction on crossings. Several types of beyond-planar graphs have been investigated, such as k-planar graphs where every edge is crossed at most k times and RAC graphs where edges can cross only at a right angle in a straight-line drawing. A graph is optimal if the number of edges coincides with the density for its type. Optimal graphs are special and are known only for some types of beyond-planar graphs, including 1-planar, 2-planar, and RAC graphs.

For all types of beyond-planar graphs for which optimal graphs are known, we compute the range for optimal graphs, establish combinatorial properties, and show that every graph is a topological minor of an optimal graph. Note that the minor property is well-known for general beyond-planar graphs.

Downloads

Published

2023-04-20

How to Cite

Brandenburg, F. (2023). On Optimal Beyond-Planar Graphs. Computing in Geometry and Topology, 2(1), 3:1–3:15. https://doi.org/10.57717/cgt.v2i1.10

Issue

Section

Original Research Articles

Categories