On the existence of a point subset with a specified number of interior points
نویسندگان
چکیده
An interior point of a nite point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k 1, let g(k) be the smallest integer such that every set of points in the plane, no three collinear, containing at least g(k) interior points has a subset of points containing exactly k interior points. We prove that g(1) = 1, g(2) = 4, g(3) 8, and g(k) k + 2; k 4. We also give some related results.
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عنوان ژورنال:
- Discrete Mathematics
دوره 241 شماره
صفحات -
تاریخ انتشار 2001