Combinatorial Coloring of 3-Colorable Graphs

@article{Kawarabayashi2012CombinatorialCO,
  title={Combinatorial Coloring of 3-Colorable Graphs},
  author={Ken-ichi Kawarabayashi and Mikkel Thorup},
  journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science},
  year={2012},
  pages={68-75}
}
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 Õ(n<sup>4/11</sup>) colors. This is the first combinatorial improvement of Blum's Õ(n<sup>3/8</sup>) bound from FOCS'90. Like Blum's algorithm, our new algorithm composes nicely with recent semi-definite programming approaches. The current best bound is Õ(n<sup>0.2072</sup>) colors by Chlamtac from FOCS'07. We now bring it down to O… CONTINUE READING