You can compute the max-flow of an undirected graph. The edges have capacities and in the undirected case you assume that capacity can be used in both 'directions'.
Also, the problem is to find a global min-cut, which requires all-pairs max flow.
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.