Variant of proof in textbook.

Proof sketch:

- 1.
- TSP
NP

Given a tour, check that each vertex is visited exactly once and the sum of costs k - 2.
- L' = HC
- 3.
- HC
TSP

Given graph*G*= (*V*,*E*), transformation*f*outputs complete graph with vertices*V*.

Weights of edges = 1 if , or (|V| + 1) if

Also outputs the number |V|.

*f*is clearly implementable in polynomial time. - 4.
- Then there exists a tour in this complete graph of size iff there exists a Hamiltonian Cycle in original graph.

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