More on the crossing number of [formula omitted]: Monotone drawings

Abstract

The Harary-Hill conjecture states that the minimum number of crossings in a drawing of the complete graph Kn is Z(n):=14⌊n2⌋⌊n−12⌋⌊n−22⌋⌊n−32⌋. 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.