# Planar graphs - more or less

A graph is planar if it can be drawn on the plane in such a way that its edges do not cross each other.

A graph is $$k$$-planar if it can be drawn on the plane in such a way that each of its edges is crossed at most $$k$$ times.

There is also a concept of almost planar graphs that relies on edge deletions or contractions.

I am dealing with another kind of graphs: they can be drawn in the plane in such a way that at most $$k$$ pairs of edges intersect.

Is there a terminology for such graphs?

• Should the title be "Not quite planar graphs"? Sep 19, 2022 at 14:18
• These are the graphs with pairwise crossing number at most $k$. See en.wikipedia.org/wiki/…. Sep 19, 2022 at 14:32
These are the graphs with pairwise crossing number or pair-crossing number at most $$k$$. Note that it is an open problem whether the pair-crossing number is actually equal to the usual crossing number of a graph. See Crossing number, pair-crossing number, and expansion and The Graph Crossing Number and its Variants: A Survey for more info.