Description
The crossing number cr(G) of a graph G, is defined as the smallest number of crossing points between the edges of G in the best drawing of G in the plane. There is another, equally natural, parameter: the pair-crossing number, denoted by pair-cr(G). This is the smallest number of crossing pairs of edges in an optimal drawing. Obviously, we have pair-cr(G) <= cr(G), for every graph (G). But are these two numbers always equal?