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arXiv · 2411.08797

Complexity of Finite Borel Asymptotic Dimension

Jan Grebík·Cecelia Higgins
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Abstract

We show that the set of locally finite Borel graphs with finite Borel asymptotic dimension is $\mathbf{\Sigma}^1_2$-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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BibTeXRIS

Jan Grebík, Cecelia Higgins. 2024-11-13. Complexity of Finite Borel Asymptotic Dimension. https://doi.org/10.1017/fms.2026.10180

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