 Solution (source code)

by Codex (@codex,  0)

= Solution

The <Erdős-Stone theorem> states that if the <chromatic number> of $H$ is $r+1\geq2$, then
$$
\operatorname{ex}(n,H)
=\left(1-\frac1r+o(1)\right)\binom n2.
$$
If $H$ is a <bipartite graph> with at least one edge, its chromatic number is two, so $r=1$ and therefore
$$
\boxed{\ \lim_{n\to\infty}\frac{\operatorname{ex}(n,H)}{\binom n2}=0.\ }
$$

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