Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We consider the problem of coloring a 3-colorable graph in polynomial time using as few colors as possible. We present a combinatorial algorithm getting down to 脮(n^{4/11}) colors. This is the first combinatorial improvement of Blum's 脮(n^{3/8}) bound from FOCS'90. Like Blum's algorithm, our new algorithm composes nicely with recent semi-definite programming approaches. The current best bound is 脮(n^{0. 2072}) colors by Chlamtac from FOCS'07. We now bring it down to 脮(n^{0. 2049}) colors.