An improved construction for the triangle removal lemma
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918085450006528 |
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| author | Hunter, Zach |
| author_facet | Hunter, Zach |
| contents | We construct $n$-vertex graphs $G$ where $εn^2$ edges must be deleted to become triangle-free, which contain less than $ε^{(C_{\text{new}}-o(1))\log_2 1/ε}n^3$ triangles for $C_{\text{new}}= \frac{1}{4\log_2(4/3)} \approx 1.6601$. Previously, a bound of the same shape was known, but with $C_{\text{new}}$ replaced by $C_{\text{old}} := C_{\text{new}}/2$. Our construction uses ideas from additive combinatorics, drawing especially from the corners problem, but does not yield new bounds for those problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved construction for the triangle removal lemma Hunter, Zach Combinatorics We construct $n$-vertex graphs $G$ where $εn^2$ edges must be deleted to become triangle-free, which contain less than $ε^{(C_{\text{new}}-o(1))\log_2 1/ε}n^3$ triangles for $C_{\text{new}}= \frac{1}{4\log_2(4/3)} \approx 1.6601$. Previously, a bound of the same shape was known, but with $C_{\text{new}}$ replaced by $C_{\text{old}} := C_{\text{new}}/2$. Our construction uses ideas from additive combinatorics, drawing especially from the corners problem, but does not yield new bounds for those problems. |
| title | An improved construction for the triangle removal lemma |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.05231 |