Let C be a collection of n compact convex sets in the plane, such that the boundaries of any pair of sets in C intersect in at most s points, for some constant s. We show that the maximum number of regular vertices (intersection points of two boundaries that intersect twice) on the boundary of the union U of C is O * (n 4/3 ), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.
['Esther Ezra', 'János Pach', 'Micha Sharir']
On regular vertices on the union of planar objects