@article{Brandenburg_2023, title={On Optimal Beyond-Planar Graphs}, volume={2}, url={https://cgt-journal.org/index.php/cgt/article/view/10}, DOI={10.57717/cgt.v2i1.10}, abstractNote={<p>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.</p>
<p>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.</p>}, number={1}, journal={Computing in Geometry and Topology}, author={Brandenburg, Franz}, year={2023}, month={Apr.}, pages={3:1–3:15} }