Empty Triangles in Generalized Twisted Drawings of K_n

Simple drawings are drawings of graphs in the plane such that vertices are distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect at most once (either in a proper crossing or in a shared endpoint). Simple drawings are generalized twisted if there is a point O such that every ray emanating from O crosses every edge of the drawing at most once, and there is a ray emanating from O which crosses every edge exactly once. We show that all generalized twisted drawings of K_n contain exactly 2n − 4 empty triangles, by this making a substantial step towards proving the conjecture that any simple drawing of K_n contains at least 2n − 4 empty triangles.