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Hamiltonian Cycle Problem

A Hamiltonian Cycle is a simple cycle in a graph going through each vertex exactly once.

HC = { $\langle$ G $\rangle \vert$ G has a Hamiltonian cycle}

Theorem 34.13: HC $\in$ NPC

Proof:

1.
Done earlier.
2.
L' = VERTEX-COVER
3.
VERTEX-COVER \(\leq_P\) HC
4.
x $\in$ VERTEX-COVER $\leftrightarrow$ f(x) $\in$ HC
Proof is complex.

Alternate proof: Reduce from 3-CNF-SAT (1st edition).


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