Groups, Geometry, and Dynamics
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Published online: 2013-01-31
Measurable chromatic and independence numbers for ergodic graphs and group actionsClinton T. Conley and Alexander S. Kechris (1) Cornell University, Ithaca, USA
(2) California Institute of Technology, Pasadena, United States
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.
Keywords: Ergodic actions, Borel combinatorics, chromatic numbers, amenable groups, free groups
Conley Clinton, Kechris Alexander: Measurable chromatic and independence numbers for ergodic graphs and group actions. Groups Geom. Dyn. 7 (2013), 127-180. doi: 10.4171/GGD/179