A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in   Chordal Graphs
  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. 
Mamadou Moustapha Kant\'e and Vincent Limouzy and Arnaud Mary and   Lhouari Nourine and Takeaki Uno
cs.DS cs.DM