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

HC = { G G has a Hamiltonian cycle}

**Theorem 34.13: HC **** NPC**

Proof:

- 1.
- Done earlier.
- 2.
- L' = VERTEX-COVER
- 3.
- VERTEX-COVER HC
- 4.
- x
VERTEX-COVER
f(x)
HC

Proof is complex.

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