Q1: A common mistake was to claim that there are at most m distinct
st-dipaths in a digraph (where m is the number of arcs). Maybe there was
some misunderstanding about distinct dipaths and disjoint dipaths.
Q2: In this question, many students were implicitly assuming that for each
u and v there was at most one arc (uv or vu). Also, they should explain
exactly how to update a flow when pushing flow through a path in the case
there are arcs uv and vu in the digraph.
Many students also used flow decomposition for non integer flows. Note that
the theorem in the course notes is for integer flows, so they should
provide a proof for the non-integer case.
Q4: In this question, many used negative capacities. This is not allowed
for max st-flows.
Q5: This question was OK. The most common mistake was to forget to prove
that every set of k node-disjoint st-dipaths yields a feasible flow of
value k.