Polynomial-delay enumeration of minimal connected dominating sets in chordal bipartite graphs

Establish a polynomial-delay algorithm for enumerating the minimal connected dominating sets of chordal bipartite graphs.

Background

The paper proves an incremental-polynomial-time algorithm for enumerating minimal connected dominating sets in chordal bipartite graphs by exploiting the bounded conformality of the hypergraph of minimal separators. Improving this result to polynomial delay remains unresolved. The authors note that doing so may require a different strategy or progress on minimal-transversal enumeration for bounded-dimension hypergraphs.

References

We leave open the existence of polynomial-delay algorithms for Dom-Enum and TDom-Enum in bipartite graphs, and for CDom-Enum in chordal bipartite graphs. Concerning this last case, we note that obtaining polynomial delay is open for Trans-Enum on hypergraph of bounded dimension, which define a proper subclass of hypergraphs of bounded conformality.

— Enumerating minimal dominating sets and variants in chordal bipartite graphs  (2502.14611 - Castelo et al., 20 Feb 2025) in Section 6, “Discussion”