When I was trying to solve a problem, I met another problem like this:
Given a undirected connected graph $G=(V,E)(|V|\le100)$ and some subgraphs of $G$: $G_1,G_2,\cdots,G_n(n\le 32)$, and all $G_i$ is connected and include all the vertexs in $G$. We need to cut some edges in $G$ so that neither of the subgraphs $G_1,G_2,\cdots,G_n$ is a connected graph. What's the minimum number of edges we need to cut?
I have tried many ways but all failed. Could anyone please give me an algorithm to solve it? :)