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Universal graphs

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

A countable graph G is called “universal” for a property P if G contains any countable graph H in P as a subgraph. The most remarkable example of a universal graph is the Rado graph, also known as the “infinite random graph”. In general the universal graph need not always exist, so the natural question to ask is, for which properties one can find such a graph. I’m going to discuss recent results, which settle this question for a property of not containing a given finite subtree.

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

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