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The Hajnal-Szemeredi Theorem and sporting events

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If you have a question about this talk, please contact Anton Evseev.

A classical result of Hajnal and Szemeredi states that an oriented graph with $nk$ vertices and maximal degree st most $n-1$ can be properly coloured so that each colour class contains precisely $n$ vertices. I will sketch a recent short proof of this result due to Kierstead and Kostochka and will explain how it could be used to arrange a fair draw in a competition. If time allows, I will also mentioned some problems motivated by this possible application.

This talk is part of the Junior Algebra and Number Theory seminar series.

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