Binary set systems and totally balanced hypergraphs

François Brucker (1, 2) , Pascal Préa (1, 2) , Célia Châtel (1, 2)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle

We show in this paper that totally balanced hypergraphs (hypergraphs which do not contain special cycles) are exactly hypergraphs that are embeddable into closed hypergraphs for which each vertex admits at most two sons (so called binary hypergraphs). To prove this result we exhibit an efficient algorithm which can produce any binary hypergraph and adapt it to binarize a given totally balanced hypergraph. This result gives, like Lehel[9], a constructive characterization of totally balanced hypergraph.

Mots clés: hypergraphs; totally balanced hypergraphs; binary hypergraphs

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]

François Brucker, Pascal Préa, Célia Châtel. Binary set systems and totally balanced hypergraphs. 2020. ⟨hal-02436247v1⟩