Question: Pseudocode or written explanation only. Consider a network with capacities c(e) over edges. Say that we found the maximum flow function from s to t.

Pseudocode or written explanation only.

Consider a network with capacities c(e) over edges. Say that we found the maximum flow function from s to t. Denote by f(e) the flow on e. Say that we choose one of the directed edges e and increase the capacity of this edge e by 1. Namely the capacity of e is c(e) + 1 now. In the following 4 questions each can be true or false. Hence answer for each one of them if its true or false and prove your answer.

1) It may be that the flow value was not increased even after the change.

2) It may be that the flow value icnreased by 2 after the change.

3) It may be that the flow increased by 1 after the change.

4) It is possible to find in time O(m + n) if the current flow f is still a maximum flow, or otherwise find a new maximum flow. Here |V| = n and |E| = n.

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