Borel fractional colorings of Schreier graphs
Annales Henri Lebesgue, Volume 5 (2022), pp. 1151-1160.

Metadata

Keywordsfractional coloring, Borel sets, Borel combinatorics, Schreier graph, group action, symbolic dynamics

Abstract

Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ2 Γ (with respect to some finite subset FΓ). 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.


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