Critical 3-Hypergraphs
Abstract
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.
Domains
Combinatorics [math.CO]
Origin : Files produced by the author(s)