Geodesic
Measure-theoretic unfriendly colorings
Clinton T. Conley1
1 Department of Mathematics Cornell University Ithaca, NY 14853, U.S.A.
Fundamenta Mathematicae, Tome 226 (2014) no. 3, pp. 237-244 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm226-3-3
Keywords: consider problem finding measurable unfriendly partition vertex set locally finite borel graph standard probability space after isolating sufficient condition existence partition settles dynamical analog problem weak equivalence graphs induced measure preserving actions groups designated finite generating set corollary obtain existence translation invariant random unfriendly colorings cayley graphs finitely generated groups

Clinton T. Conley 1

1 Department of Mathematics Cornell University Ithaca, NY 14853, U.S.A. 
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Clinton T. Conley. Measure-theoretic unfriendly colorings. Fundamenta Mathematicae, Tome 226 (2014) no. 3, pp. 237-244. doi: 10.4064/fm226-3-3

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