Complexity of Finite Borel Asymptotic Dimension
Abstract
We show that the set of locally finite Borel graphs with finite Borel asymptotic dimension is 12-complete. The result is based on a combinatorial characterization of finite Borel asymptotic dimension for graphs generated by a single Borel function. As an application of this characterization, we classify the complexities of digraph homomorphism problems for this class of graphs.
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