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                * Princeton Discrete Math Seminar *
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Speaker: Robert Simon, LSE

Thursday 3rd April, 3:00 in Fine Hall 224.

Title: Proper graph colouring, optimization, and paradoxical decompositions

We show that there is an infinite graph of finite degree defined by a
Borel equivalence relation on a probability space such that it can be 
coloured properly with 17 colours but only in ways that induce 
paradoxical decompositions. We also show that there are problems of 
optimization such that every epsilon-optimal solution for small enough 
positive epsilon induces a paradoxical decomposition.

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