The lonely runner problem for many runners

2011/06/12 by Artūras Dubickas · 11 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #Mathematics

paper · pdf · doi:10.3336/gm.46.1.05

published in Glasnik Matematicki 46(1), 25-30 (University of Zagreb)

openalex publication_date 2011/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The lonely runner conjecture asserts that for any positive integer n and any positive numbers v 1 < < vn there exists a positive number t such that ||v i t|| 1/(n + 1) for every i = 1, . . . , n. We verify this conjecture for n 16342 under assumption that the speeds of the runners satisfy v j+1 v j 1 + 33 log n n for j = 1, . . . , n -1.

Citations

• Flows, View Obstructions, and the Lonely Runner
• View-obstruction problems, III
• Untere Schranken f�r zwei diophantische Approximations-Funktionen
• View-obstruction problems in n-dimensional geometry
• The Lonely Runner with Seven Runners
• View-obstruction: a shorter proof for 6 lonely runners
• On the chromatic number of circulant graphs
• Zwei S�tze �ber inhomogene diophantische Approximation von Irrationalzehlen
• Six Lonely Runners

Cited by

• Correlation Among Runners and Some Results on the Lonely Runner Conjecture
• Lonely runner conjecture [wikipedia]