Prime 3-uniform hypergraphs - Archive ouverte HAL
Article Dans Une Revue Graphs and Combinatorics Année : 2021

Prime 3-uniform hypergraphs

Abderrahim Boussaïri
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Brahim Chergui
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Pierre Ille
Mohamed Zaidi
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Résumé

Given a 3-uniform 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-uniform hypergraph is prime if all its modules are trivial. Given a prime 3-uniform hypergraph, we study its prime, 3-uniform and induced subhypergraphs. Our main result is: given a prime 3-uniform hypergraph H, with V (H) ≥ 4, there exist v, w ∈ V (H) such that H − {v, w} is prime.

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Dates et versions

hal-03362671 , version 1 (01-10-2021)

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Abderrahim Boussaïri, Brahim Chergui, Pierre Ille, Mohamed Zaidi. Prime 3-uniform hypergraphs. Graphs and Combinatorics, 2021, 37 (6), pp.2737-2760. ⟨10.1007/s00373-021-02391-w⟩. ⟨hal-03362671⟩
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