Question: 5. Let G be a connected graph with at least one edge. (a) {5 marks} Prove that each vertex of G' is saturated by some

5. Let G be a connected graph with at least one edge. (a) {5 marks} Prove that each vertex of G' is saturated by some maximum matching in G. (b) {4 marks} Provide a counterexample with explanations for each of the following: 1. Every edge of G' is in some maximum matching of G. ii. Every vertex of G is in some minimum cover of G

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