For each of the following subproblems, briefly explain how you would solve each

For each of the following subproblems, briefly explain how you would solve each. You do not need to write pseudocode. Give a big-O estimate on your solution with a very brief justification.

Given a graph G=(V,E) with n nodes and m edges, determine the number of connected components in G.

Given a connected graph G=(V,E) with n nodes and m edges, determine whether it is possible to color all of the nodes in V either blue or gold such that if (v,w)∈E, then v and w do not have the same color.