Polynomial-delay enumeration of minimal dominating sets in bipartite graphs

Establish whether the minimal dominating sets of arbitrary bipartite graphs can be enumerated with polynomial delay.

Background

Minimal dominating set enumeration is known to admit strong algorithms on several restricted graph classes, including chordal bipartite graphs as established by this paper. The corresponding complexity for general bipartite graphs remains unresolved, despite the importance of bipartite incidence graphs in relating domination enumeration to minimal transversal enumeration.

References

Still the problem is not known to admit a polynomial-delay algorithm.

— Enumerating minimal dominating sets and variants in chordal bipartite graphs  (2502.14611 - Castelo et al., 20 Feb 2025) in Section 1, paragraph beginning “Note that, in the literature”

Still the problem is not known to admit a polynomial-delay algorithm.

— Enumerating minimal dominating sets and variants in chordal bipartite graphs  (2502.14611 - Castelo et al., 20 Feb 2025) in Section 1, paragraph beginning “Note that, in the literature”