More on the crossing number of Kn: Monotone drawings

The Harary-Hill conjecture states that the minimum number of crossings in a drawing of the complete graph Kn is . This conjecture was recently proved for 2-page book drawings of Kn. As an extension of this technique, we prove the conjecture for monotone drawings of Kn, that is, drawings where all vertices have different x-coordinates and the edges are x-monotone curves.