  Let $\Gamma$ be a finite graph, and for each vertex $i$ let $G_i$ be a
finitely presented group. Let $G$ be the graph product of the $G_i$. That is,
$G$ is the group obtained from the free product of the $G_i$ by factoring out
by the smallest normal subgroup containing all $[g,h]$ where $g\in G_i$ and
$h\in G_j$ and there is an edge joining i and j . We show that $G$ has an
isoperimetric function of degree $k\ge 2$ (or an exponential isoperimetric
function) if each vertex group has such an isoperimetric function.
