The Breakdown of Complexity: What Happens When Triangles in a Network Vanish?

Suppose you were a chemist who is studying a particular reaction, where you have chemical medium with abundant pairwise bonds, but three-body reactions are energetically suppressed. As a chemist you want to understand how much of a particular molecule which contain these three body reactions can be produced by such a chemical soup.

But as a chemist, you understand it is highly unlikely you will be able to get too much information by studying one particular batch of the chemical soup, and you are more likely to gain a better understanding regarding the situation looking at the large scale statistical behavior. But how do you do this?

This is where extremal combinatorics is