Equality of crossing and pair-crossing numbers

Determine whether the crossing number equals the pair-crossing number for every graph, or, failing equality, establish a universal constant c > 0 such that the pair-crossing number is at most c times the crossing number for every graph.

Background

The crossing number counts crossing points, whereas the pair-crossing number counts pairs of edges that cross. In an optimal drawing for the crossing number, two edges cross at most once, but the two parameters may still differ because their minimizing drawings need not coincide.

The paper identifies equality as a major open problem and gives the weaker bounded-ratio formulation as an alternative. The best known general estimate is only an upper bound of order crossing number to the 3/2 power times a logarithmic factor.