Distributed (Delta + 1)-coloring in linear (in Delta) time

@article{Barenboim2014Distributed,
  title={Distributed (Delta + 1)-coloring in linear (in Delta) time},
  author={Leonid Barenboim and Michael Elkin},
  journal={SIAM J. Comput.},
  year={2014},
  volume={43},
  pages={72-95}
}
The distributed (∆ + 1)-coloring problem is one of most fundamental and well-studied problems of Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current state-of-the-art running time is O(∆ log ∆ + log∗ n), due to Kuhn and Wattenhofer, PODC’06. Linial (FOCS’87) has proved a lower bound of 
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