Measure-theoretic unfriendly colorings

Clinton T. Conley. "Measure-theoretic unfriendly colorings." Fundamenta Mathematicae 226.3 (2014): 237-244. <http://eudml.org/doc/282985>.

@article{ClintonT2014,
abstract = {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.},
author = {Clinton T. Conley},
journal = {Fundamenta Mathematicae},
keywords = {unfriendly partitions; Borel combinatorics; weak equivalence},
language = {eng},
number = {3},
pages = {237-244},
title = {Measure-theoretic unfriendly colorings},
url = {http://eudml.org/doc/282985},
volume = {226},
year = {2014},
}

TY - JOUR
AU - Clinton T. Conley
TI - Measure-theoretic unfriendly colorings
JO - Fundamenta Mathematicae
PY - 2014
VL - 226
IS - 3
SP - 237
EP - 244
AB - 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.
LA - eng
KW - unfriendly partitions; Borel combinatorics; weak equivalence
UR - http://eudml.org/doc/282985
ER -