Counting minimal transversals of β-acyclic hypergraphs

We prove that one can count in polynomial time the number of minimal transversals of $\beta$-acyclic hypergraphs. As 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, TAMC'17].