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SOLVED: Texts: 2Exercise 2. Recall the combinatorial optimization problem described in S3.3, the minimum vertex cover problem for a non-bipartite graph. For a non-bipartite graph, the corresponding integer program has a constraint matrix that is not necessarily unimodular, and thus the solution to the LP relaxation need not be an integer vector. Consider the following graph:25152.6fsa) Set up the integer program that corresponds to the minimum vertex cover problem.b) Solve the LP relaxation (int

From the proof of Theorem 34.12, we know that the vertex-cover problem and the NP-complete clique problem are complementary in the sense that an optimal vertex cover is the complement of a maximum-size clique in the complement graph. Does this relationship imply that there is a polynomial-time approximation algorithm with a constant approximation ratio for the clique problem? Justify your answer. | Numerade

3.1.1. (-) Find a maximum matching in each graph below. Prove that it is a maximum matching by exhibiting an optimal solution to the dual problem (minimum vertex cover). Explain why this proves that the matching is optimal.