A stronger LOCAL model supporting Marks’ obstruction

Construct a nontrivial stronger variant of the LOCAL model in which all LCL problems known to admit Borel solutions are efficiently solvable, while 3-coloring acyclic graphs of maximum degree 3 remains impossible by Marks’ method.

Background

Marks’ method yields strong Borel lower bounds, but the ordinary LOCAL model only captures a limited finite analogue because algorithms inspect bounded-radius neighborhoods. The paper asks whether a stronger yet nontrivial model can incorporate unbounded-distance information without making 3-coloring on degree-3 forests solvable.

References

Is there a stronger variant of the LOCAL model (e.g., for which all the LCL problems that are known to admit a Borel solution are efficiently solvable, see ) so that $3$-coloring of acyclic graphs of degree at most $3$ is still not possible, because of Marks' method?

— From descriptive to distributed  (2502.15347 - Grebík et al., 21 Feb 2025) in Problem 6.3, Section 6 (Generalizations)