An Isoperimetric Function for Bestvina-Brady Groups

Given a right-angled Artin group A, the associated Bestvina-Brady group is defined to be the kernel of the homomorphism A \to $\mathbb{Z}$ that maps each generator in the standard presentation of A to a fixed generator of $\mathbb{Z}$. We prove that the Dehn function of an arbitrary finitely presented Bestvina-Brady group is bounded above by n^4. This is the best possible universal upper bound.