Prove that there exists constant k such that, for all $5v < e$ there is a subgraph of the complete graph of $v$ vertics with crossing number less or equal than $ k e^3/v^2$.
Any hints for a way to apply probabilistic argument ?
Prove that there exists constant k such that, for all $5v < e$ there is a subgraph of the complete graph of $v$ vertics with crossing number less or equal than $ k e^3/v^2$.
Any hints for a way to apply probabilistic argument ?
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You may want to look at crossing number inequality of this link.