2020/06/25 by Abderrahim Boussaïri, Boussairi, Abderrahim, Brahim Chergui +5
Decision Sciences · Mathematics · #05C65 #05C75 #05C76 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2006.14527
openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a 3-hypergraph H, a subset M of V(H) is a module of H if for each e∈ E(H) such that e∩ M≠∅ and e∖ M≠∅, there exists m∈ M such that e∩ M=\m\ and for every n∈ M, we have (e∖\m\)∪\n\∈ E(H). For example, ∅, V(H) and \v\, where v∈ V(H), are modules of H, called trivial. A 3-hypergraph is prime if all its modules are trivial. Furthermore, a prime 3-hypergraph is critical if all its induced subhypergraphs, obtained by removing one vertex, are not prime. We characterize the critical 3-hypergraphs.