np-complete


How to reduce 3COLOR to 3SAT?


We know that 3SAT ≤p 3COLOR(i.e. 3SAT is polynomial time reducible to 3COLOR).
Can anyone give a short argument why 3COLOR ≤p 3SAT?
And give an actual Cook reduction showing that 3COLOR ≤p 3SAT Please.
the short answer is: since 3SAT is NP-complete, any problem in NP can be p.t. reduced to
solving an instance of 3SAT (or showing it is not satisfiable). Hence 3COLOR <=p 3SAT.
For a construction of p.t. reduction of 3COLOR to SAT, you may see section 2 in the
following document (the topic is not related to your question):
http://research.microsoft.com/apps/pubs/default.aspx?id=66816

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