On regular vertices on the union of planar objects

Authors:
Esther Ezra;Janos Pach;Micha Sharir
Affiliations:
Tel Aviv University, Tel Aviv, Israel;New York University, New York, NY;Tel Aviv University, Tel Aviv, Israel
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

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Abstract

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*(n4/3), which improves earlier bounds due to Aronov et.al.The bound is nearly tight in the worst case.