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≤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