The lonely runner with seven runners
Combinatorics
2007-10-25 v1 Number Theory
Abstract
Suppose 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 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 (). 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.
Cite
@article{arxiv.0710.4495,
title = {The lonely runner with seven runners},
author = {J. Barajas and O. Serra},
journal= {arXiv preprint arXiv:0710.4495},
year = {2007}
}