Borel fractional colorings of Schreier graphs
Copyright policy )Borel fractional colorings of Schreier graphs
Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ↷2 Γ (with respect to some finite subset F⊆Γ). We show that the Borel fractional chromatic number of G is equal to 1 over the measurable independence number of G. As a consequence, we asymptotically determine the Borel fractional chromatic number of G when Γ is the free group, answering a question of Meehan.
- Georgia Institute of Technology United States
Symbolic dynamics, Mathematics - Logic, Dynamical Systems (math.DS), Borel combinatorics, Schreier graph, Coloring of graphs and hypergraphs, symbolic dynamics, Dynamical systems involving maps of trees and graphs, fractional coloring, FOS: Mathematics, Borel sets, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Dynamical Systems, group action, Logic (math.LO), Descriptive set theory
Symbolic dynamics, Mathematics - Logic, Dynamical Systems (math.DS), Borel combinatorics, Schreier graph, Coloring of graphs and hypergraphs, symbolic dynamics, Dynamical systems involving maps of trees and graphs, fractional coloring, FOS: Mathematics, Borel sets, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Dynamical Systems, group action, Logic (math.LO), Descriptive set theory
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