Andras Sebö
Laboratoire Leibniz-IMAG, Grenoble
Resumo: Suppose k runners having nonzero constant speeds run laps on a unit-length circular track. Then there is a time at which all runners are at least 1/(k+1) from their common starting point. We call this the ``Lonely Runner Conjecture'', and prove it for k < 5. Besides the proof I would like to show the connection of this problem to several different combinatorial problems, among them to network flows. (This is joint work with Bienia, Goddyn, Gvozdiak and Tarsi).