On: Solving the minimum cut problem for undirected gra...

[eutectic]

Also, the problem is to find a global min-cut, which requires all-pairs max flow.

[gloria_mundi → eutectic]

Not actually all-pairs max flow, you can fix the source and consider all possible sinks. In the AoC problem we also know that the min-cut is 3, so we can abort the flow algorithm as soon as we have found a 4-flow.