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}

HC $\in$ NPC

Proof:

1.

Done earlier.

2.

L' = 3-CNF-SAT

3.

3-CNF-SAT HC

4.

x $\in$ 3-CNF-SAT $\leftrightarrow$ f(x) $\in$ HC
Proof is complex.