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Threshold function for a graph not being planar
A graph property $\mathcal{P}$ is monotone increasing if $G\in \mathcal{P}$ implies $G+e \in \mathcal{P}$, i.e., adding an edge to a graph does not destroy the property.
It is well-known that every ...
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is there an example in planar graph that using probabilistic methods
The probabilistic method is a technique for proving the
existence of an object with certain properties by showing that
a random object chosen from an appropriate probability
distribution has the ...