Convex Quadrilaterals and k-Sets
نویسندگان
چکیده
We prove that the minimum number of convex quadrilaterals determined by n points in general position in the plane – or in other words, the rectilinear crossing number of the complete graph Kn – is at least ( 38 + 10 −5) ( n 4 ) +O(n). Our main tool is a lower bound on the number of (≤ k)-sets of the point set: we show that for every k ≤ n/2, there are at least 3 ( k+1 2 ) subsets of size at most k that can be separated from their complement by a straight line.
منابع مشابه
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تاریخ انتشار 2003