论文信息 - Lower Bounds for the Number of Small Convex k-Holes

Lower Bounds for the Number of Small Convex k-Holes

Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h"k(n) of convex k-holes in S, and give improved lower bounds on h"k(n), for 3==n^2-32n7+227, h"4(n)>=n^22-9n4-o(n), and h"5(n)>=3n4-o(n). We further settle several questions on sets of 12 points posed by Dehnhardt in 1987.

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