Erdős Problem #626

`g k n` is \(g_k(n)\): the largest \(m\) such that some graph on \(n\) vertices has chromatic number exactly \(k\) and girth \(> m\), that is, no cycle of length \(\leq m\). The girth is `SimpleGraph.egirth`, which is `⊤` for an acyclic graph. The value `sSup ∅ = 0` for \(n < k\) affects only finitely many \(n\). For \(k \leq 2\) the set is unbounded whenever an acyclic graph on \(n\) vertices with chromatic number \(k\) exists, and then `sSup` is also \(0\); this case is not used below, where \(k \geq 4\).

`h m n` is \(h^{(m)}(n)\): the largest chromatic number of a graph on \(n\) vertices with girth \(> m\).