  Graph associahedra are generalized permutohedra arising as special cases of
nestohedra and hypergraphic polytopes. The graph associahedron of a graph $G$
encodes the combinatorics of search trees on $G$, defined recursively by a root
$r$ together with search trees on each of the connected components of $G-r$. In
particular, the skeleton of the graph associahedron is the rotation graph of
those search trees. We investigate the diameter of graph associahedra as a
function of some graph parameters. We give a tight bound of $\Theta(m)$ on the
diameter of trivially perfect graph associahedra on $m$ edges. We consider the
maximum diameter of associahedra of graphs on $n$ vertices and of given
tree-depth, treewidth, or pathwidth, and give lower and upper bounds as a
function of these parameters. We also prove that the maximum diameter of
associahedra of graphs of pathwidth two is $\Theta (n\log n)$. Finally, we give
the exact diameter of the associahedra of complete split and of unbalanced
complete bipartite graphs.
