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日期：2025-10-23 08:36

Graph Algorithms and Complexity Theory
Semester 1 Session 2025–2026
In the network below capacities are indicated by numbers next to the edges. Compute a maximum
flow in this network, state its value, and find a minimum cut, the edges across this cut, and state
the cut’s capacity. Show your work.
The 56 marks available split as follows:
40 marks for a correct maximum flow explicitly given together with some evidence (augmenting
paths, residual networks) on how it was found
16 marks for a correct maximum flow reconstructed from the augmenting paths used
1 mark for each augmenting path and each residual network if no maximum flow was found. The
total number of marks for these paths and networks is rounded down to the next integer and
capped at 6.
4 mark for the value of the last flow found, independent of its maximality
4 mark for a minimum cut
4 mark for the set of edges across the given cut, independent of its minimality
4 mark for the capacity of the given cut, independent of its minimality
Submit your work in Gradescope before the deadline on Monday 27 October 2025, 10am. This
piece of summative coursework is worth 7% of your final grade.