Division of a graph into connected subgraphs with sets of vertices that must be in the same subgraph

Question

I have a connected, undirected graph G = (V, E), a set S = {S_1, S_2, ..., S_n}, where each S_i is a subset of V and ak> 1. How can I split V into k subsets such , which is guaranteed that:

• for each i, each node in S_i is in the same subset
• each subset is a connected subgraph of G?

Answer 1

G = (V, E) (s ₁, t ₁),..., (s _m, t _m), H G , s _i t _i H.

- , , . , - NP-.

, , , , c, , k = | V | - c, S _i= {s _i, t _i}. c, , | V | - c = k. , , , | V | - k = c.

2, , k . , , .

Answer 2

. , S_i, S_j, . , , S_k - , . , . k , , , . , n ^ k, , . , "" S, .

, , . ;)