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{\bf J. Barajas and O. Serra}
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{\bf The Lonely Runner with Seven Runners}
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Suppose $k+1$ runners having nonzero constant pairwise distinct 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.



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