On the Pseudolinear Crossing Number

4 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that 5 each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing 6 number c̃r(G) of a graph G is the minimum number of pairwise crossings of edges in 7 a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing 8 number, including its computational complexity and its relationship to the usual cross9 ing number and to the rectilinear crossing number. This investigation was motivated 10 by open questions and issues raised by Marcus Schaefer in his comprehensive survey 11 of the many variants of the crossing number of a graph. 12