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 Z 2 * 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.

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The word problem for Thompson's group F has a solution, but it remains unknown whether F is automatic or has a finite or regular convergent (terminating and confluent) rewriting system. We show that the group F admits a natural extension of these two properties, namely autostackability, and we give an explicit bounded regular convergent prefix-rewriting system for F .