Geodesic
The lonely runner with seven runners
The electronic journal of combinatorics, Tome 15 (2008)
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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.
DOI : 10.37236/772
Classification : 11B75, 11J71, 05C15
Mots-clés : view obstruction problems 
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     author = {J. Barajas and O. Serra},
     title = {The lonely runner with seven runners},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/772},
     zbl = {1206.11030},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/772/}
}
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J. Barajas; O. Serra. The lonely runner with seven runners. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/772

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