Empty pentagons in point sets with collinearities
نویسندگان
چکیده
An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328` points in the plane contains an empty pentagon or ` collinear points. This is optimal up to a constant factor since the (` − 1) × (` − 1) grid contains no empty pentagon and no ` collinear points. The previous best known bound was doubly exponential.
منابع مشابه
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2015