Erdős Problem #766

\(f(n;k,l)\) in the sense of [Er64c], where it is called \(f_1(n;k,l)\): the least \(m\) such that every graph with \(n\) vertices and \(m\) edges contains at least one graph with \(k\) vertices and \(l\) edges as a (not necessarily induced) subgraph. There is no graph with \(n\) vertices and more than \(\binom{n}{2}\) edges, so the set is nonempty.

The function of erdosproblems.com: the minimum of \(\mathrm{ex}(n;G)\) over all graphs \(G\) with \(k\) vertices and \(l\) edges. In [Er64c] the least \(m\) such that every graph with \(n\) vertices and \(m\) edges contains one fixed graph with \(k\) vertices and \(l\) edges is called \(f_2(n;k,l)\), so this is \(f_2(n;k,l) - 1\). The value is in `ℕ∞` and is `⊤` when no such graph \(G\) exists.