The GOAL is to create a way of getting sequence of graphs with the following properties:

1. \(girth \to \infty\)
2. Embeds into cubes
3. \(deg(v) \in [3,M] ~\forall v \in X\)

Let \(g_{n}\) be the girth of \(X_{n}\). Any cube of size \(< 2^{g_{n}}\) can not contain a loop.