$(\Delta + 1)$ Vertex Coloring in $O(n)$ Communication
<|reference_start|>$(\Delta + 1)$ Vertex Coloring in $O(n)$ Communication: We study the communication complexity of $(\Delta + 1)$ vertex coloring, where the edges of an $n$-vertex graph of maximum degree $\Delta$ are partitioned between two players. We provide a randomized protocol which uses $O(n)$ bits of communication and ends with both players knowing the coloring. Combining this with a folklore $\Omega(n)$ lower bound, this settles the randomized communication complexity of $(\Delta + 1)$-coloring up to constant factors.<|reference_end|>
@article{flin2024$(\delta,
    title={$(\Delta + 1)$ Vertex Coloring in $O(n)$ Communication},
    author={Maxime Flin and Parth Mittal},
    journal={arXiv preprint arXiv:2404.19081},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.19081},
    primaryClass={cs.DS}
}