(a) Let G = ( (W,B), E) be a bipartite graph. Explain why W is a vertex-cover of G.
(b) Analogously, it can be shown that B is a vertex-cover of G. Is W or B always the minimum vertex-cover of G?
If your answer is yes, explain why.
If your answer is no, give a bipartite graph G = ( (W,B), E) where neither W nor B is a minimum vertex-cover. Give a vertex-cover Q different from W and B, and a matching M to show that Q is minimum.