Counting Minimal Transversals of $\beta$-Acyclic Hypergraphs

Benjamin Bergougnoux; Florent Capelli; Mamadou Moustapha Kant\'e

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Counting Minimal Transversals of $\beta$-Acyclic Hypergraphs

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arxiv 1808.05017 v1 pith:5NT5ZWRK submitted 2018-08-15 cs.DS

Benjamin Bergougnoux , Florent Capelli , Mamadou Moustapha Kanté This is my paper · ORCID

classification cs.DS

keywords minimalacyclicbetacountcountingdominatinghypergraphsnumber

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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].

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