An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing the set of minimal hitting sets in hypergraphs. We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and well-studied graph class where such an algorithm was open for a while.
@article{arxiv.1407.2036,
title = {A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs},
author = {Mamadou Moustapha Kanté and Vincent Limouzy and Arnaud Mary and Lhouari Nourine and Takeaki Uno},
journal= {arXiv preprint arXiv:1407.2036},
year = {2014}
}