BROOKS’ THEOREM FOR MEASURABLE COLORINGS

DOI10.1017/fms.2016.14OpenAlexW3099253507MaRDI QIDQ5739905

Clinton T. Conley, Robin D. Tucker-Drob, Andrew S. Marks

Publication date: 6 July 2016

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.03361

Mathematics Subject Classification ID

Descriptive set theory (03E15) Combinatorial probability (60C05) Ergodic theory on groups (22D40) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Coloring of graphs and hypergraphs (05C15)

Related Items (11)

Borel combinatorics fail in HYP ⋮ Local problems on grids from the perspective of distributed algorithms, finitary factors, and descriptive combinatorics ⋮ On the almost eigenvectors of random regular graphs ⋮ Distributed algorithms, the Lovász local lemma, and descriptive combinatorics ⋮ Correlation Bounds for Distant Parts of Factor of IID Processes ⋮ Marked groups with isomorphic Cayley graphs but different Borel combinatorics ⋮ Measurable versions of Vizing's theorem ⋮ Equivalence relations that act on bundles of hyperbolic spaces ⋮ Measurable versions of the Lovász local lemma and measurable graph colorings ⋮ Equitable colourings of Borel graphs ⋮ On Baire measurable colorings of group actions

Cites Work

• On invariant ccc \(\sigma\)-ideals on \(2^{\mathbb N}\)
• Perfect matchings as IID factors on non-amenable groups
• A measurable-group-theoretic solution to von Neumann's problem
• Minimal spanning forests
• Ends of graphed equivalence relations. I
• Ends of graphed equivalence relations. II
• Borel chromatic numbers
• Critical percolation on any nonamenable group has no infinite clusters
• Topics in orbit equivalence
• Measurable chromatic and independence numbers for ergodic graphs and group actions
• Processes on unimodular random networks
• Towards a theory of negative dependence
• A determinacy approach to Borel combinatorics
• COUNTABLE BOREL EQUIVALENCE RELATIONS
• The graph-theoretic approach to descriptive set theory
• Ultraproducts of measure preserving actions and graph combinatorics

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