Measurable-Borel equivalence for linear-growth classes
Determine whether, for every class F of bounded-degree graphs of linear growth, an LCL problem is measurably solvable on measured graphs locally in F if and only if it is Borel solvable.
References
Is it true that an LCL problem on ${\bf F}$ can be solved measurably on measured graphs that are locally in ${\bf F}$ if and only if it can be solved in a Borel way?
— From descriptive to distributed
(2502.15347 - Grebík et al., 21 Feb 2025) in Problem 8, Section 7 (LCL problems)
Let ${\bf F}$ be a class of graphs of bounded degree and linear growth. Is it true that an LCL problem on ${\bf F}$ can be solved measurably on measured graphs that are locally in ${\bf F}$ if and only if it can be solved in a Borel way?
— From descriptive to distributed
(2502.15347 - Grebík et al., 21 Feb 2025) in Problem 8, Section 11 (Open problems), LCL problems