Hyperfiniteness and Borel combinatorics

@article{Conley2019HyperfinitenessAB,
  title={Hyperfiniteness and Borel combinatorics},
  author={Clinton T. Conley and Steve Jackson and Andrew S. Marks and Brandon Seward and Robin D. Tucker-Drob},
  journal={Journal of the European Mathematical Society},
  year={2019}
}
We study the relationship between hyperfiniteness and problems in Borel graph combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite setting. We compute the possible Borel chromatic numbers and edge chromatic numbers of bounded degree acyclic hyperfinite Borel graphs and use this to answer a question of Kechris and Marks about the relationship between Borel chromatic number and measure chromatic number. We also show that for every $d > 1$ there is a $d… 

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