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Number of segments and triangles inequality

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December 6, 2010
inequalitiescombinatorics proposedcombinatoricsgraph theoryExtremal combinatorics

Problem Statement

In space are given n≥2n\ge 2 points, no four of which are coplanar. Some of these points are connected by segments. Let KK be the number of segments (K>1)(K>1) and TT be the number of formed triangles. Prove that 9T2<2K39T^2<2K^3.
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