Counting Minimal Transversals of $\beta$-Acyclic Hypergraphs

TL;DR

This paper demonstrates that counting minimal transversals in beta-acyclic hypergraphs can be done efficiently, enabling polynomial-time counting of minimal dominating sets in strongly chordal graphs, advancing graph theory algorithms.

Contribution

It introduces a polynomial-time counting method for minimal transversals in beta-acyclic hypergraphs, extending to minimal dominating sets in strongly chordal graphs.

Findings

Counting minimal transversals in beta-acyclic hypergraphs is polynomial-time feasible.

Polynomial-time counting of minimal dominating sets in strongly chordal graphs is achieved.

Extends previous research on minimal dominating sets in specific graph classes.

Abstract

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. Kant\'e and T. Uno, Counting Minimal Dominating Sets, TAMC'17].