Triangles in a Complete Graph

Discrete Mathematics Level 4

A straight-line drawing of a graph \(G\) is a drawing of \(G\) on the plane such that all its edges are straight line segments.

The maximum number of triangles that can be found in a straight-line drawing of the complete graph \(K_4 \) is 8, as seen in the image. For \( K_5 \), there can be up to 35 triangles.

What is the maximum number of triangles that can be found in a straight-line drawing of the complete graph \(K_{10} \)?

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Daniel Liu by Daniel Liu
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