(1) Let G = (V, E) be an undirected graph with d components, where |V| = b and |E| =c  . Please prove that c ≥ b − d . (10%)

(2) Consider the complete bipartite graphKm,n , where the vertex set is partitioned into two disjoint sets V1 and V2with |V1 | = m and |V2 | = n. Derive the necessary and sufficient conditions for ? and ? such that Km，n contains an Eulerian path but NO Eulerian circuit. (Consider all possible cases for m and n ). (10%)