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A simple graph G on n vertices (n ?2) is drawn in the plane. Prove...

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A simple graph G on n vertices (n ?2) is drawn in the plane. Prove that if every edge crosses at most one another edge, then the number of edges in G does not exceed 4n - 8.

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Transcribed Image Text

A simple graph G on n vertices (n ?2) is drawn in the plane. Prove that if every edge crosses at most one another edge, then the number of edges in G does not exceed 4n - 8.

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