Abstract
Let COLk be the set of all k-colorable graphs. It is easy to show that if a<b then COLa \le COLb (poly time reduction). Using the Cook-Levin theorem it is easy to show that if 3 \le a< b then COLb \le COLa. However this proof is insane in that it translates a graph to a formula and then the formula to a graph. We give a simple proof that COLk \le COL3.
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