More on the crossing number of : Monotone drawings

The Harary-Hill conjecture states that the minimum number of crossings in a drawing of the complete graph K n is Z ( n ) : = 1 4 ⌊ n 2 ⌋ ⌊ n − 1 2 ⌋ ⌊ n − 2 2 ⌋ ⌊ n − 3 2 ⌋ . This conjecture was recently proved for 2-page book drawings of K n . 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.