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\title{\bf Assignment 6 \\[2ex]
\rm\normalsize CS 581 \\ Due November 29, 2018}
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\paragraph{Problem 1 [10 point]}
Prove that the decision problem variant of the Travelling Salesman Problem you defined in your last
assignment is NP-Complete. (You've already proven it's in NP, so you only need to show the reduction)

\paragraph{Problem 2 [10 point]}
Show that if the decision problem variant of TSP has a poly-time solution then the optimization problem
variant of TSP also has a poly-time solution.

\paragraph{Problem 3 [10 point]}
Co-NP is the class of the complements of the problems in NP. For example, since SAT is in NP, its
complement:
\[\{x \;|\; x \text{ is a formula that is not satisfiable} \}\]

is in Co-NP. Co-NP-complete problems are
defined in the usual way. It is not known whether or not Co-NP and NP are the same classes of problems.
Show that, if NP and Co-NP are different, then P and NP are also different.


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