Congruence-relation lattices of optiongraphs

Determine which lattices can arise as the lattice of congruence relations of an optiongraph.

Background

The paper proves that the congruence relations of every optiongraph form a complete lattice under inclusion. It does not characterize the class of complete lattices that can occur in this way. The unresolved problem is therefore to determine the possible lattice structures realized by optiongraphs.

References

What lattices can arise as the lattice of congruence relations of an optiongraph?

— Isomorphism Theorems for Impartial Combinatorial Games  (2505.04919 - Baltushkin et al., 8 May 2025) in Question following Example in Section 2, “Quotient optiongraphs”