  We show that the free factor complex of the free group of rank at least 3
does not satisfy a combinatorial isoperimetric inequality: that is, for every N
greater than or equal to 3, there is a loop of length 4 in the free factor
complex that only bounds discs containing at least O(N) triangles. To prove the
result, we construct a coarsely Lipschitz function from the `upward link' of a
free factor to the set of integers.
