A Sane Proof that COLk \le COL3
Computational Complexity
2016-01-29 v2 Combinatorics
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.
Cite
@article{arxiv.1407.5128,
title = {A Sane Proof that COLk \le COL3},
author = {William Gasarch},
journal= {arXiv preprint arXiv:1407.5128},
year = {2016}
}