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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...
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| Published in: | Graphs and combinatorics 2023-02, Vol.39 (1), Article 3 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | 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. |
|---|---|
| ISSN: | 0911-0119 1435-5914 |
| DOI: | 10.1007/s00373-022-02595-8 |