Extremal graph theory

If a microscopic K5 knot ruins planarity, what happens if we intentionally force a massive amount of edges into a network?

We enter the realm of extremal graph theory.

Exactly.

But before we hit the density thresholds, Distal links this to graph coloring.

So in a perfect graph, the local clique density perfectly predicts the global coloring need?

Right.

But as you mentioned, coloring is the primer for extremal graph theory.

Right.