  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 if every edge is crossed at most k times and RAC
if 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.
