Maximum flow using Ford-Fulkerson and DFS This question is about the time complexity of the Ford-Fulkerson
maximum flow algorithm when using DFS to find augmenting paths.

There is a well-known example showing that using DFS one can need a
linear number of iterations in the maximum flow, see for instance the
Wikipedia page linked to above.

However, I'm not really convinced by this example: a standard DFS
implementation would not exhibit the behaviour of alternating between B and C as
first node of the path (using the vertex names from the Wikipedia page).

So, let us impose the very natural condition that whenever the DFS visits a node
$u$, it always examines the neighbors of $u$ in the same order.  Are there
still examples for which FF with DFS uses a large number of
iterations?

As a variant, suppose that we have the additional property that the
different orderings of neighbors are consistent with some arbitrary
but fixed global ordering of the vertices.  Does that make a
difference?

This seems to me like a pretty basic question; I apologize in advance
if the answer is well-known but I am not an expert on flows and some
googling did not turn up anything.

Edit:
The answer turns out to be yes, there are still examples.  See Figure 2 of this paper.  In these examples FF with DFS take an exponential (in the number of vertices) number of iterations.  It seems easy to prove that this is tight, i.e., that the number of iterations are always bounded by $2^{O(n)}$ (regardless of the values of the capacities).
If adjacency lists are fixed in advance then DFS always terminates (even if there are irrational capacities).

See Dean, Goemans, Immorlica -- Finite Termination of "Augmenting Path" Algorithms in the Presence of Irrational Problem Data.