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Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics

Hypergraph Turán Problem of the Generalized Triangle with Bounded Matching Number

  • Jian Wang
  • Wenbin Wang
  • Weihua Yang
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Abstract

Let ℋ be a 3-graph on n vertices. The matching number ν(ℋ) is defined as the maximum number of disjoint edges in ℋ. The generalized triangle F5 is a 3-graph on the vertex set {a,b,c,d,e} with the edge set {abc, abd,cde}. In this paper, we determine the maximum number of edges in an F5-free $3$-graph ℋ satisfying ν(ℋ)≤ s when n≥ 30(s+1). More precisely, the maximum is binomn−12 for s=1,2 and is s⌊ (n−s)2/4⌋ for s≥ 3. We also determine the unique extremal graph for each case. For the proof, we establish a 2-colored version of Mantel's theorem, which may be of independent interest.

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Cite

BibTeXRIS
BibTeX
@article{wang2026hypergraph,
  title = {{Hypergraph Turán Problem of the Generalized Triangle with Bounded Matching Number}},
  author = {Jian Wang and Wenbin Wang and Weihua Yang},
  journal = {The Electronic Journal of Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.37236/14444},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p18},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Hypergraph Turán Problem of the Generalized Triangle with Bounded Matching Number
AU  - Jian Wang
AU  - Wenbin Wang
AU  - Weihua Yang
PY  - 2026
DA  - 2026/10/23
JO  - The Electronic Journal of Combinatorics
DO  - 10.37236/14444
UR  - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p18
AB  - Let ℋ be a 3-graph on n vertices. The matching number ν(ℋ) is defined as the maximum number of disjoint edges in ℋ. The generalized triangle F_5 is a 3-graph on the vertex set {a,b,c,d,e} with the edge set {abc, abd,cde}. In this paper, we determine the maximum number of edges in an F_5-free $3$-graph ℋ satisfying ν(ℋ)≤ s when n≥ 30(s+1). More precisely, the maximum is binomn−12 for s=1,2 and is s⌊ (n−s)^2/4⌋ for s≥ 3. We also determine the unique extremal graph for each case. For the proof, we establish a 2-colored version of Mantel's theorem, which may be of independent interest.
SN  - 1077-8926
ER  -