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

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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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## This note was uploaded on 07/14/2011 for the course COT 4610 taught by Professor Dutton during the Fall '10 term at University of Central Florida.

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

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