Cuts, labelling procedure and max-flow min-cut Quiz

1. Arcs: SB 5, AT 4 and BA 7 (from B to A). What is the capacity of the cut $X=\{S,A\}$, $Y=\{B,T\}$?

• A. $16$
• B. $11$
• C. $9$
• D. $5$

2. An arc has capacity $10$ and flow $4$. What labels does the labelling procedure show?

• A. $4$ forward and $6$ backward
• B. $10$ forward and $4$ backward
• C. $6$ forward and $10$ backward
• D. $6$ forward and $4$ backward

3. A flow of value $15$ is found, and a cut has capacity $15$. What can you conclude?

• A. The flow can be increased
• B. The flow is maximum and the cut is minimum
• C. The cut is not a valid cut
• D. Nothing can be concluded

4. What is true at every vertex other than the source and sink?

• A. Flow in equals flow out
• B. Capacity in equals capacity out
• C. Flow equals capacity
• D. Flow in is greater than flow out

5. A flow-augmenting route has spare capacities $5$, $3$ and $4$. By how much does the flow increase?

• A. $12$
• B. $5$
• C. $3$
• D. $4$