An interior point of a finite 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. Similarly, for any integer k ≥ 3, let h(k) be the smallest integer such that every set of points in the plane, no three collinear, containing at least h(k) interior points has a subset of points containing exactly k or k+1 interior points. In this note, we show that g(k) ≥ 3k - 1 for k ≥ 3. We also show that h(k) ≥ 2k + 1 for 5 ≤ k ≤ 8, and h(k) ≥ 3k - 7 for k ≥ 8. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Fevens, T. (2003). A note on point subsets with a specified number of interior points. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2866, 152–158. https://doi.org/10.1007/978-3-540-44400-8_15
Mendeley helps you to discover research relevant for your work.