Many Empty Triangles have a Common Edge
نویسندگان
چکیده
Given a finite point set X in the plane, the degree of a pair {x, y} ⊂ X is the number of empty triangles t = conv{x, y, z}, where empty means t∩X = {x, y, z}. Define degX as the maximal degree of a pair in X. Our main result is that if X is a random sample of n independent and uniform points from a fixed convex body, then degX ≥ cn/ lnn in expectation.
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 50 شماره
صفحات -
تاریخ انتشار 2013