Output-sensitive enumeration of total and connected minimal dominating sets in bipartite graphs

Determine whether minimal total dominating sets and minimal connected dominating sets in arbitrary bipartite graphs can be enumerated with polynomial delay or, more generally, in output-polynomial time.

Background

The total and connected variants of minimal domination are closely related to minimal-transversal enumeration but are more difficult because connected domination involves minimal separators. The paper reports that, even for bipartite graphs, neither polynomial-delay enumeration nor output-polynomial enumeration is known for these variants.

References

Concerning TDom-Enum and CDom-Enum, it is also open, to the best of our knowledge, whether they can be solved with polynomial delay, or even in output-polynomial time, in bipartite graphs.

— Enumerating minimal dominating sets and variants in chordal bipartite graphs  (2502.14611 - Castelo et al., 20 Feb 2025) in Section 1, paragraph beginning “Concerning TDom-Enum and CDom-Enum”