A Turán-type theorem on chords of a convex polygon (Q1204472)
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scientific article; zbMATH DE number 130567
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Turán-type theorem on chords of a convex polygon |
scientific article; zbMATH DE number 130567 |
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A Turán-type theorem on chords of a convex polygon (English)
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10 March 1993
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The paper proves that the maximum number of straight line segments connecting \(n\) points in convex position in the plane such that no \(k+1\) of them are pairwise crossing is \({n \choose 2}\) if \(n \leq 2k+1\) and \(2kn-{2k+1 \choose 2}\) if \(n \geq 2k+1\).
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chords
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convex polygon
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maximum number
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straight line segments
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