VC_to_HC_copy - (2 Create a cycle with all the"a"...

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VC Hamiltonian Cycle VC: Instance: a graph G = (V, E) and an integer k. Question: Does there exist S V such that (1) |S| ≤ k, and (2) every edge has at least one endpoint in S? Let G = (V, E) and k be an arbitrary instance of VC. We will now create a new graph H = (V', E') as follows: (1) For each edge (a, b) of E, construct a "component" on 12 vertices as follows: 1 input/output vertices 2 3 4 5 6 input/output vertices "a" vertices "b" vertices Note: the "non input/output" vertices will not be adjacent to any other vertices in H.
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Unformatted text preview: (2) Create a cycle with all the "a" vertices by adding an edge between the last of one component to the first a of the next component (the order of components is unimportant). Repeat for every vertex in G. (3) Add an additional k vertices z 1 , z 2 , …, z k . Add edges from each of these to every input/output vertex. This is the graph H and is an instance of Hamiltonian Cycle....
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