Hyperfinite acyclic Borel graph coloring complexity

Determine whether the class of Δ-regular acyclic hyperfinite Borel graphs with Borel chromatic number at most Δ is Σ¹₂-complete.

Background

The paper connects the question to the strong failure of Brooks-type theorems in the Borel context and to the complexity of hyperfinite Borel graphs.

References

Do $\Delta$-regular acyclic Borel hyperfinite Borel graphs that have Borel chromatic number at most $\Delta$ form a $\Sigma1_2$-complete?

— From descriptive to distributed  (2502.15347 - Grebík et al., 21 Feb 2025) in Problem 11, Section 7 (Complexity)