I have a computational problem that I want to solve. I'm not sure if it has already been studied in literature, or if so under what name. I'd appreciate any pointers to literature or suggestions for an algorithm.
Input: A connected, undirected graph G = (V, E) in which certain edges are labelled "bad".
Output: The minimum cardinality partition of V such that 1) all of the induced subgraphs of the partition are connected, and 2) none of the induced subgraphs contains a bad edge.