27. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 3 + 3 = 6
28. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 3 + 3 = 6
29. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 3 + 4 - 1 = 6
30. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 3 + 4 - 1 = 6
31. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 4 + 2= 6
32. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 4 + 2= 6
33. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 4 + 2= 6
34. Observation 1
The network flow sent across any cut is equal to the
amount reaching sink.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
total flow = 6, flow on cut = 4 + 2= 6
35. Observation 2
Then the value of the flow is at most the capacity of
any cut.
4
2 4
3 4
1 4 6
8 3
3 5
2
It’s trivial!
36. Observation 2
Then the value of the flow is at most the capacity of
any cut.
4
2 4
3 4
1 4 6
8 3
3 5
2
It’s trivial!
37. Observation 3
Let f be a flow, and let (S,T) be an s-t cut whose
capacity equals the value of f.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
f is the maximum flow
(S,T) is the minimum cut
38. Observation 3
Let f be a flow, and let (S,T) be an s-t cut whose
capacity equals the value of f.
4/4
2 4
3/3 4/4
1 1/4 6
3/8 2/3
3 5
2/2
f is the maximum flow
(S,T) is the minimum cut