We consider the problem of coloring graphs of maximum degree Δ with Δ colors in the distributed setting with limited bandwidth. Specifically, we give a polyloglogn-round randomized algorithm in the CONGEST model. This is close to the lower bound of Ω(loglogn) rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lov\'asz local lemma (LLL) and the deg+1-list coloring problem.
@article{arxiv.2405.09975,
title = {Distributed Delta-Coloring under Bandwidth Limitations},
author = {Yannic Maus and Magnús M. Halldórsson},
journal= {arXiv preprint arXiv:2405.09975},
year = {2024}
}