Turán Problems for Berge-(k, p)-Fan Hypergraph
Let F be a graph. A hypergraph ℋ is Berge- F if there is a bijection f : E ( F ) → E ( ℋ ) such that e ⊂ f ( e ) for every e ∈ E ( F ). A hypergraph is Berge- F -free if it does not contain a subhypergraph isomorphic to a Berge- F hypergraph. The authors denote the maximum number of hyperedges in an...
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| Published in | Chinese annals of mathematics. Serie B Vol. 42; no. 4; pp. 487 - 494 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2021
Springer Nature B.V Department of Mathematics,Shanghai University,Shanghai 200444,China%School of Management,Shanghai University,Shanghai 200444,China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9599 1860-6261 |
| DOI | 10.1007/s11401-021-0272-7 |
Cover
| Summary: | Let F be a graph. A hypergraph
ℋ
is Berge-
F
if there is a bijection
f
:
E
(
F
)
→
E
(
ℋ
)
such that
e
⊂
f
(
e
) for every
e
∈
E
(
F
). A hypergraph is Berge-
F
-free if it does not contain a subhypergraph isomorphic to a Berge-
F
hypergraph. The authors denote the maximum number of hyperedges in an
n
-vertex
r
-uniform Berge-
F
-free hypergraph by
ex
r
(
n
, Berge-
F
).
A (
k, p
)-fan, denoted by
F
k,p
, is a graph on
k
(
p
− 1) + 1 vertices consisting of
k
cliques with
p
vertices that intersect in exactly one common vertex. In this paper they determine the bounds of
ex
r
(
n
, Berge-
F
) when
F
is a (
k, p
)-fan for
k
≥ 2,
p
≥ 3 and
r
≥ 3. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0252-9599 1860-6261 |
| DOI: | 10.1007/s11401-021-0272-7 |