The graph structure of graph groups that are subgroups of Thompson’s group V

We determine exactly which graph products, also known as Right Angled Artin Groups, embed into Richard Thompson’s group V. It was shown by Bleak and Salazar-Diaz that ℤ2 ∗ ℤ was an obstruction. We show that this is the only obstruction. This is shown by proving a graph theory result giving an alternate description of simple graphs without an appropriate induced subgraph.