List colourings and preference orders

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• Andrew Thomason (University of Cambridge)
• Thursday 04 May 2017, 14:30-15:30
• MR12.

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

The list chromatic number of a hypergraph G is the smallest number k such that, for any assignment to each vertex of G of a list of k colours, it is possible for each vertex to choose a colour from its list so that no edge is monochromatic. Alon showed that the list chromatic number of a graph is of order at least log d, where d is the average degree. Saxton et at did the same for r-uniform hypergraphs, using the container method.

Is the lower bound best possible? Using a notion of “preference orders” we examine the list chromatic numbers of multipartite hypergraphs, showing thereby that the lower bound is best possible for r=2 and r=3 but probably not for r>=4. This is joint work with Arès Méroueh.

This talk is part of the Combinatorics Seminar series.

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