VC_to_HC

VC_to_HC - component to the first a of the next component...

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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. (2) Create a cycle with all the "a" vertices by adding an edge between the last of one
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Unformatted text preview: 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. (a, b) a d G = b c VC = {a, c}, or {b, c} (a, c) z 1 (b, c) z 2 (c, d)...
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VC_to_HC - component to the first a of the next component...

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