Hypergraph Turán problem of the generalized triangle with bounded matching number
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913954862727168 |
|---|---|
| author | Wang, Jian Wang, Wenbin Yang, Weihua |
| author_facet | Wang, Jian Wang, Wenbin Yang, Weihua |
| contents | Let $\mathcal{H}$ be a 3-graph on $n$ vertices. The matching number $ν(\mathcal{H})$ is defined as the maximum number of disjoint edges in $\mathcal{H}$. 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 showed that an $F_5$-free 3-graph $\mathcal{H}$ with matching number at most $s$ has at most $s\lfloor (n-s)^2/4\rfloor$ edges for $n\geq 30(s+1)$ and $s\geq 3$. For the proof, we establish a 2-colored version of Mantel's theorem, which may be of independent interests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypergraph Turán problem of the generalized triangle with bounded matching number Wang, Jian Wang, Wenbin Yang, Weihua Combinatorics Let $\mathcal{H}$ be a 3-graph on $n$ vertices. The matching number $ν(\mathcal{H})$ is defined as the maximum number of disjoint edges in $\mathcal{H}$. 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 showed that an $F_5$-free 3-graph $\mathcal{H}$ with matching number at most $s$ has at most $s\lfloor (n-s)^2/4\rfloor$ edges for $n\geq 30(s+1)$ and $s\geq 3$. For the proof, we establish a 2-colored version of Mantel's theorem, which may be of independent interests. |
| title | Hypergraph Turán problem of the generalized triangle with bounded matching number |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.04579 |