Output-polynomial enumeration for additional graph classes

Determine whether minimal dominating sets can be enumerated in output-polynomial time on comparability graphs, graphs with no induced $C_4$, and graphs with no induced $2K_3$.

Background

Minimal Dominating Set Enumeration is a special case of Dualization. The paper notes that polynomial-delay or output-polynomial-time algorithms are known for several graph classes, including chordal graphs, $K_t$-free graphs for fixed $t$, and certain graphs of bounded structural parameters.

Despite these positive results, the cited literature leaves output-polynomial-time enumeration unresolved for comparability graphs, graphs with no induced $C_4$, and graphs with no induced $2K_3$. These classes are discussed as concrete boundaries for extending tractability results.