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 references therein for more info.

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.