Peer-reviewedCC BYThe Electronic Journal of Combinatorics
Nine and Ten Lonely Runners
- 1University of Oxford
Abstract
The Lonely Runner Conjecture of Wills and Cusick states that if k+1 runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least 1/(k+1) away from all other runners. Rosenfeld recently obtained a computer-assisted proof of the conjecture for $8$ runners. By refining his approach with a sieve, we obtain proofs (also computer-assisted) for $9$ and $10$ runners.
Related
BibTeX
@article{trakulthongchai2026nine,
title = {{Nine and Ten Lonely Runners}},
author = {Tanupat Trakulthongchai},
journal = {The Electronic Journal of Combinatorics},
year = {2026},
month = jun,
doi = {10.37236/14972},
url = {https://doi.org/10.37236/14972},
note = {CC BY},
}
RIS
TY - JOUR
TI - Nine and Ten Lonely Runners
AU - Tanupat Trakulthongchai
PY - 2026
DA - 2026/06/05
JO - The Electronic Journal of Combinatorics
DO - 10.37236/14972
UR - https://doi.org/10.37236/14972
AB - The Lonely Runner Conjecture of Wills and Cusick states that if k+1 runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least 1/(k+1) away from all other runners. Rosenfeld recently obtained a computer-assisted proof of the conjecture for $8$ runners. By refining his approach with a sieve, we obtain proofs (also computer-assisted) for $9$ and $10$ runners.
SN - 1077-8926
SN - 1097-1440
ER -