Geodesic
Measurable chromatic and independence numbers for ergodic graphs and group actions
Clinton T. Conley1 ; Alexander S. Kechris2
1Cornell University, Ithaca, USA
2California Institute of Technology, Pasadena, United States
Groups, geometry, and dynamics, Tome 7 (2013) no. 1, pp. 127-180

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DOI

We study in this paper combinatorial problems concerning graphs generated by measure preserving actions of countable groups on standard measure spaces. In particular we study chromatic and independence numbers, in both the measure-theoretic and the Borel context, and relate the behavior of these parameters to properties of the acting group such as amenability, Kazhdan’s property (T), and freeness. We also prove a Borel analog of the classical Brooks’ Theorem in finite combinatorics for actions of groups with finitely many ends.
DOI : 10.4171/ggd/179
Classification : 03-XX, 05-XX, 22-XX, 37-XX
Mots-clés : Ergodic actions, Borel combinatorics, chromatic numbers, amenable groups, free groups

Clinton T. Conley  1   ; Alexander S. Kechris  2

1 Cornell University, Ithaca, USA
2 California Institute of Technology, Pasadena, United States 
Clinton T. Conley; Alexander S. Kechris. Measurable chromatic and independence numbers for ergodic graphs and group actions. Groups, geometry, and dynamics, Tome 7 (2013) no. 1, pp. 127-180. doi: 10.4171/ggd/179
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     title = {Measurable chromatic and independence numbers for ergodic graphs and group actions},
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     pages = {127--180},
     year = {2013},
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     doi = {10.4171/ggd/179},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/179/}
}
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