2 4 A ug 2 00 6 New lower bounds for the number of ( ≤ k ) - edges and the rectilinear crossing number of K n ∗
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چکیده
We provide a new lower bound on the number of (≤ k)-edges of a set of n points in the plane in general position. We show that for 0 ≤ k ≤ ⌊ 2 ⌋ the number of (≤ k)-edges is at least Ek(S) ≥ 3 (
منابع مشابه
A ug 2 00 6 New lower bounds for the number of ( ≤ k ) - edges and the rectilinear crossing number of K n ∗
We provide a new lower bound on the number of (≤ k)-edges of a set of n points in the plane in general position. We show that for 0 ≤ k ≤ ⌊ 2 ⌋ the number of (≤ k)-edges is at least Ek(S) ≥ 3 (
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We provide a new lower bound on the number of (≤ k)-edges of a set of n points in the plane in general position. We show that for 0 ≤ k ≤ bn−2 2 c the number of (≤ k)-edges is at least Ek(S) ≥ 3 ( k + 2 2 ) + k ∑ j=b3 c (3j − n + 3), which, for b3 c ≤ k ≤ 0.4864n, improves the previous best lower bound in [11]. As a main consequence, we obtain a new lower bound on the rectilinear crossing numbe...
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We use circular sequences to give an improved lower bound on the minimum number of (≤ k)– sets in a set of points in general position. We then use this to show that if S is a set of n points in general position, then the number (S) of convex quadrilaterals determined by the points in S is at least 0.37533 ` n 4 ́ + O(n). This in turn implies that the rectilinear crossing number cr(Kn) of the com...
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تاریخ انتشار 2009