2-Coloring Cycles in One Round
Distributed, Parallel, and Cluster Computing
2026-03-06 v2 Formal Languages and Automata Theory
Abstract
We show that there is a one-round randomized distributed algorithm that can 2-color cycles such that the expected fraction of monochromatic edges is less than 0.24118. We also show that a one-round algorithm cannot achieve a fraction less than 0.23879. Before this work, the best upper and lower bounds were 0.25 and 0.2. Our proof was largely discovered and developed by large language models, and both the upper and lower bounds have been formalized in Lean 4.
Keywords
Cite
@article{arxiv.2603.04235,
title = {2-Coloring Cycles in One Round},
author = {Maxime Flin and Alesya Raevskaya and Ronja Stimpert and Jukka Suomela and Qingxin Yang},
journal= {arXiv preprint arXiv:2603.04235},
year = {2026}
}
Comments
9 pages, 3 figures