390
3. [BB] The needs of the retail outlets cannot
be met. They can receive at most 14 units
a month, as shown.
To see that the flow
S
there is a maximum, consider the cut in which
T
=
{a, F, G, t}
and
S
is the set of all other
vertices.
4. Now the retail outlets can receive at most
13 units.
To see that the flow shown is
maximum, consider the cut in which
T
=
S
{a, F, G, t}
and
S
is the set of all other ver
tices.
Solutions to Exercises
5. (a) [BB] A maximum flow is shown on the left, with directions added to the undirected edges.
1 1
S
t
4,3
(b) A maximum flow is shown on the right, with directions added.
6. The maximum number of edge disjoint paths from
s
to
t
is
three: Observe that
sdct, sabt,
and
sfet
are three edge disjoint
paths from
s
to
t
and no more than three such paths can be
found. The minimum number of edges whose removal severs
all paths from
s
to
t
is three:
If
fewer than three edges incident
with
s
are not removed, then a path remains.
7. [BB] Four messengers can be sent.
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 Summer '10
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 Graph Theory, Glossary of graph theory, Maxflow mincut theorem, edge disjoint paths

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