  It has been shown that the edge structure of the characteristic imset
polytope is closely connected to the question of causal discovery. The diameter
of a polytope is an indicator of how connected the polytope is and moreover
gives us a hypothetical worst case scenario for an edge-walk over the polytope.
We present low-degree polynomial bounds on the diameter of
$\operatorname{CIM}_n$ and, for any given undirected graph $G$, the face
$\operatorname{CIM}_G$.
