Polychromatic colouring and cover-decomposition problems in the plane

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• Dömötör Pálvölgyi (University of Cambridge)
• Thursday 26 May 2016, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

Is it true that given a finite point set on a sphere and a set of halfspheres, such that the set system that they induce on the point set is a Sperner family, we can select a subset of the points that meet every halfsphere in at least one but at most two points? I don’t know the answer to this question (waiting to be solved by YOU !), but I know that the above holds in the plane if instead of halfspheres we take (pseudo)halfplanes. I will talk about consequences of similar results in polychromatic colouring and cover-decomposition, and also mention several other open problems.

This talk is part of the Combinatorics Seminar series.

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