I have a undirected graph with no edge costs. A subset of the nodes are labeled $c_1, c_2, ..., c_k$ and one node is labeled $K$. I want to find the minimum cut of the graph with the extra condition that all nodes $c_i$ are in the same half of the cut and the node K is in the other cut.
My idea was to begin by doing a BFS from $K$ to all nodes $c_i$, saving predecessors and then finding all paths from $K$ to a node $c_i$ and finally picking the minimum set of edges from the paths so that at least one edge from each path was chosen. Unfortunately, if I understand this correctly, this is equivalent to the NP-complete set cover problem.
Is there anything sane with this approach? Do you have any hints to push me in the right direction?
Note: this is homework so I'd rather have some hints than a full solution.