The lonely runner with seven runners
| dc.creator | Barajas, J. | |
| dc.creator | Serra, O. | |
| dc.date | 2007-10-24 | |
| dc.date.accessioned | 2026-07-07T08:38:25Z | |
| dc.date.available | 2026-07-07T08:38:25Z | |
| dc.description | Suppose $k+1$ runners having nonzero constant speeds run laps on a unit-length circular track starting at the same time and place. A runner is said to be lonely if she is at distance at least $1/(k+1)$ along the track to every other runner. The lonely runner conjecture states that every runner gets lonely. The conjecture has been proved up to six runners ($k\le 5$). A formulation of the problem is related to the regular chromatic number of distance graphs. We use a new tool developed in this context to solve the first open case of the conjecture with seven runners. | |
| dc.identifier | https://arxiv.org/abs/0710.4495 | |
| dc.identifier | http://arxiv.org/abs/0710.4495 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140726 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11B75, 11J71 | |
| dc.title | The lonely runner with seven runners | |
| dc.type | text |