On Regular Vertices of the Union of Planar Convex Objects
نویسندگان
چکیده
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), which improves earlier bounds due to Aronov et al. [4]. The bound is nearly tight in the worst case.
منابع مشابه
A convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 41 شماره
صفحات -
تاریخ انتشار 2009