Triple systems with bounded matching number: some constructions and exact Turán number
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908668580069376 |
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| author | Chen, Nannan Liu, Miao Qi, Yuzhen Yang, Caihong |
| author_facet | Chen, Nannan Liu, Miao Qi, Yuzhen Yang, Caihong |
| contents | We study the Turán numbers of $3$-graphs avoiding $3$-graphs $F$ and $M_{s+1}^3$, a matching of size $s+1$. We disprove a conjecture of Gerbner, Tompkins, and Zhou [European Journal of Combinatorics, 2025, 127:104155] on $\ex(n,\{F,M^3_{s+1}\})$ for $3$-graph $F$ with $χ(F)=2$ by constructing infinitely many counterexamples. For this family, we determine the asymptotic Turán number via edge-colored Turán problem. In addition, for the $3$-graph $F_{3,2}$ with edge set $\{123,145,245,345\}$, we determine the exact value of $\ex(n,\{F_{3,2}, M_{s+1}^3\})$ for every integers $s$ and all $n \ge 12s^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Triple systems with bounded matching number: some constructions and exact Turán number Chen, Nannan Liu, Miao Qi, Yuzhen Yang, Caihong Combinatorics We study the Turán numbers of $3$-graphs avoiding $3$-graphs $F$ and $M_{s+1}^3$, a matching of size $s+1$. We disprove a conjecture of Gerbner, Tompkins, and Zhou [European Journal of Combinatorics, 2025, 127:104155] on $\ex(n,\{F,M^3_{s+1}\})$ for $3$-graph $F$ with $χ(F)=2$ by constructing infinitely many counterexamples. For this family, we determine the asymptotic Turán number via edge-colored Turán problem. In addition, for the $3$-graph $F_{3,2}$ with edge set $\{123,145,245,345\}$, we determine the exact value of $\ex(n,\{F_{3,2}, M_{s+1}^3\})$ for every integers $s$ and all $n \ge 12s^2$. |
| title | Triple systems with bounded matching number: some constructions and exact Turán number |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.17000 |