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Measure-theoretic unfriendly colorings

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Conley C.

Fundamenta Mathematicae

2014

tom 226

nr 3

237-244

We consider the problem of finding a measurable unfriendly partition of the vertex set of a locally finite Borel graph on standard probability space. After isolating a sufficient condition for the existence of such a partition, we show how it settles the dynamical analog of the problem (up to weak equivalence) for graphs induced by free, measure-preserving actions of groups with designated finite generating set. As a corollary, we obtain the existence of translation-invariant random unfriendly colorings of Cayley graphs of finitely generated groups.

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1 Fundamenta Mathematicae

1 Conley C.

1 2014

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Measure-theoretic unfriendly colorings