Maxime Flin · Alesya Raevskaya · Ronja Stimpert · Jukka Suomela · Qingxin Yang

Brief announcement: 2-coloring cycles in one round

PODC 2026 · 45th ACM Symposium on Principles of Distributed Computing, Egham, United Kingdom, July 2026

authors’ version arXiv.org

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.

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