Random Polynomial Graphs for Random Turán Problems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909531979644928 |
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| author | Spiro, Sam |
| author_facet | Spiro, Sam |
| contents | Bukh and Conlon used random polynomial graphs to give effective lower bounds on $\mathrm{ex}(n,\mathcal{T}^\ell)$, where $\mathcal{T}^\ell$ is the $\ell$th power of a balanced rooted tree $T$. We extend their result to give effective lower bounds on $\mathrm{ex}(G_{n,p},\mathcal{T}^\ell)$, which is the maximum number of edges in a $\mathcal{T}^\ell$-free subgraph of the random graph $G_{n,p}$. Analogous bounds for generalized Turán numbers in random graphs are also proven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08050 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Random Polynomial Graphs for Random Turán Problems Spiro, Sam Combinatorics 05C80, 05C35 Bukh and Conlon used random polynomial graphs to give effective lower bounds on $\mathrm{ex}(n,\mathcal{T}^\ell)$, where $\mathcal{T}^\ell$ is the $\ell$th power of a balanced rooted tree $T$. We extend their result to give effective lower bounds on $\mathrm{ex}(G_{n,p},\mathcal{T}^\ell)$, which is the maximum number of edges in a $\mathcal{T}^\ell$-free subgraph of the random graph $G_{n,p}$. Analogous bounds for generalized Turán numbers in random graphs are also proven. |
| title | Random Polynomial Graphs for Random Turán Problems |
| topic | Combinatorics 05C80, 05C35 |
| url | https://arxiv.org/abs/2212.08050 |