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An output-polynomial algorithm for the listing of minimal dominating sets ingraphs is a challenging open problem and is known to be equivalent to thewell-known Transversal problem which asks for an output-polynomial algorithmfor listing the set of minimal hitting sets in hypergraphs. We give apolynomial delay algorithm to list the set of minimal dominating sets inchordal graphs, an important and well-studied graph class where such analgorithm was open for a while.

A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs