A graph is [planar](https://en.wikipedia.org/wiki/Planar_graph) 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](https://en.wikipedia.org/wiki/1-planar_graph) 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](https://mathworld.wolfram.com/AlmostPlanarGraph.html) 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?



Planar graphs - more or less
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](https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)) of a graph. See [Crossing number, pair-crossing number, and expansion](https://www.sciencedirect.com/science/article/pii/S0095895604000437) and [The Graph Crossing Number and its Variants: A Survey](https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS21) for more info.


