Vertex CoverA Vertex Cover of a graph G is a set of vertices such that each edge in G is incident to at least one of these vertices. The decision vertexcover problem was proven NPC. Now, we want to solve the optimal version of the vertex cover problem, i.e., we want to find a minimum size vertex cover of a given graph. We call such vertex cover an optimal vertex cover C*. An approximate algorithm for vertex cover: The idea is to take an edge (u, v) one by one, put both vertices to C, and remove all the edges incident to u or v. We carry on until all edges have been removed. C is a VC. But how good is C? VC = {b, c, d, e, f, g}
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