Counting Minimal Transversals of $beta$-Acyclic Hypergraphs

We prove that one can count in polynomial time the number of minimal transversals of $beta$-acyclic hypergraphs. In consequence, we can count in polynomial time the number of minimal dominating sets of strongly chordal graphs, continuing the line of research initiated in [M.M. Kante and T. Uno, Counting Minimal Dominating Sets, TAMC17].