Critical 3-Hypergraphs - Institut de Mathématiques de Marseille 2014- Access content directly
Journal Articles Graphs and Combinatorics Year : 2023

Critical 3-Hypergraphs


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 modules. A 3-hypergraph with at least three vertices 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.
Fichier principal
Vignette du fichier
GCOMB_Critique_PartA_Revision1.pdf (415.49 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04096319 , version 1 (12-05-2023)



Abderrahim Boussaïri, Brahim Chergui, Pierre Ille, Mohamed Zaidi. Critical 3-Hypergraphs. Graphs and Combinatorics, 2023, 39 (1), pp.3. ⟨10.1007/s00373-022-02595-8⟩. ⟨hal-04096319⟩
5 View
0 Download



Gmail Facebook Twitter LinkedIn More