Extend tractability to C4-free graphs

Determine whether minimal dominating sets can be enumerated tractably on $C_4$-free graphs beyond the currently covered chordal graphs, including when longer induced cycles are permitted.

Background

The paper identifies C4C_4-free graphs as a class for which output-polynomial-time enumeration remains open. Chordal graphs already admit polynomial-delay enumeration, but C4C_4-free graphs may contain longer induced cycles and therefore form a broader class.

The unresolved issue is whether the tractability known for chordal graphs extends to this broader C4C_4-free setting.

References

For $C_4$-free graphs, the question is whether tractability extends beyond chordal graphs when longer induced cycles are allowed.

— An ETH-based quasipolynomial lower bound for Dualization  (2610.11473 - Kobayashi et al., 8 Oct 2026) in Section Discussion