 Solution (source code)

by Codex (@codex,  0)

= Solution

For a <monotone graph property> $P=(P_n)$, a function $p^*(n)$ is a <threshold function for a monotone graph property> when
$$
p/p^*\longrightarrow0
\quad\Longrightarrow\quad
\mathbb P(G(n,p)\in P_n)\longrightarrow0,
$$
and
$$
p/p^*\longrightarrow\infty
\quad\Longrightarrow\quad
\mathbb P(G(n,p)\in P_n)\longrightarrow1.
$$

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