Measure-theoretic unfriendly colorings

• Autorzy: Clinton T. Conley
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
• 03E15: Descriptive set theory
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 3
• Strony: 237-244

Daty

wydano

2014

Twórcy

autor

Clinton T. Conley

• Department of Mathematics, Cornell University, Ithaca, NY 14853, U.S.A.

Identyfikatory

DOI

10.4064/fm226-3-3