The Lonely Runner with Seven Runners
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 15 شماره
صفحات -
تاریخ انتشار 2008