The lonely runner conjecture holds for nine runners

2025/12/01 by Matthieu Rosenfeld, Rosenfeld, Matthieu
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2512.01912

openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We prove that the lonely runner conjecture holds for nine runners. Our proof is based on a couple of improvements of the method we used to prove the conjecture for eight runners.

Citations

• Nine and ten lonely runners
• The lonely runner conjecture holds for eight runners
• Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
• The Lonely Runner Conjecture turns 60
• The Lonely Runner Conjecture
• The lonely runner with seven runners

Cited by

• Nine and ten lonely runners

Related

• The lonely runner conjecture holds for eight runners
• Nine and ten lonely runners
• The lonely runner with seven runners
• On the time for a runner to get lonely
• Some remarks on the lonely runner conjecture