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graphs that can be embedded into the plane, i.e. that can be drawn without crossings between the lines representing edges.
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Threshold function for a graph not being planar
In the Erdős–Rényi model, the threshold for the planarity is know to be $t(n) = 1/n$. Perhaps one of the easiest ways to see this is the following.
If $p=o(1/n)$, then a straightforward union bound im …