Lesson 4D.3.3

4D.3.3 The max-flow min-cut theorem Quiz: Pearson Edexcel Further Maths, Unit 42

20 questions

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Lesson 4D.3.3, The max-flow min-cut theorem: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 42: Flows in networks, written with Revision Ninja.

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The 20 questions

  1. What does the max-flow min-cut theorem state that maximum flow equals?

    • Total arc capacity
    • Minimum cut capacity
    • Source supply value
    • Maximum cut capacity

  2. According to the max-flow min-cut theorem, when is a flow proven to be maximum?

    • Flow equals source value
    • Flow equals cut capacity
    • Cut capacity equals zero
    • Flow exceeds cut capacity

  3. What can be deduced if a network flow value equals a cut capacity?

    • It is suboptimal
    • It is minimum
    • It is maximum
    • It is invalid

  4. What must be true of forward arcs crossing a cut that proves a flow maximum?

    • Flow is zero
    • Capacity is minimised
    • Flow exceeds capacity
    • Flow equals capacity

  5. What must backward arcs carry across a cut that proves a flow maximum?

    • Full capacity
    • Zero flow
    • Maximum flow
    • Positive flow

  6. What is the upper bound for any valid network flow value regarding any cut capacity?

    • Strictly greater than
    • Independent of cuts
    • Less than or equal
    • Equal to zero

  7. What must a valid network cut always separate?

    • Source from sink
    • All nodes individually
    • Sink from source only
    • Arcs from vertices

  8. In a network with arcs S to A (4), S to B (3), A to B (2), A to T (2) and B to T (4), what is the capacity of the cut with X = {S, A, B}?

    • 8
    • 6
    • 7
    • 4

  9. In the same network, what is the maximum flow from S to T?

    • 8
    • 6
    • 7
    • 5

  10. In the same network, what is the capacity of the cut with X = {S}?

    • 6
    • 7
    • 5
    • 8

  11. In the same network, what is the capacity of the cut with X = {S, B}?

    • 10
    • 8
    • 7
    • 6

  12. A flow of 5 is found with a minimum cut of 6. What can be stated about this flow?

    • Flow is infeasible
    • Flow is maximum
    • Cut capacity is wrong
    • Flow is not maximum

  13. In the maximum flow S-A 4, S-B 2, A-B 2, A-T 2, B-T 4 of the network with arcs S to A (4), S to B (3), A to B (2), A to T (2), B to T (4), what is the net flow across the cut X = {S, A, B}?

    • 6
    • 4
    • 9
    • 3

  14. What term describes an arc with flow 2 and capacity 3 in a network?

    • Saturated
    • Critical
    • Maximal
    • Unsaturated

  15. When labelling in the same maximum flow, which vertices are labelled before the labelling stops?

    • S and A, but not B.
    • S and T.
    • S only.
    • S, A and B, but not T.

  16. Can a network flow of value 7 exist if the minimum cut capacity is 6?

    • No
    • Sometimes
    • Yes
    • Depends on arcs

  17. What happens when every forward arc of a cut is saturated with zero backward flow?

    • Flow is maximum
    • Cut is invalid
    • Flow is zero
    • Source is blocked

  18. In the network with arcs S to A (4), S to B (3), A to B (2), A to T (2) and B to T (4), the capacity of S to B is raised to 5. What is the new maximum flow?

    • 6
    • 9
    • 7
    • 8

  19. In the network with arcs S to A (4), S to B (3), A to B (2), A to T (2) and B to T (4), the capacity of A to T is reduced to 1. What is the new maximum flow?

    • 6
    • 7
    • 4
    • 5

  20. Why do two different maximum flows in the same network always share the same value?

    • Equal to min cut
    • Total arc count
    • Number of vertices
    • Source capacity limit

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