The planar Turán number of $\{K_4,Θ_5\}$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866914744438358016 |
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| author | Fang, Tao |
| author_facet | Fang, Tao |
| contents | Let $\mathcal{F}$ be a set of graphs. The planar Turán number, $ex_{\mathcal{P}}(n,\mathcal{F})$, is the maximum number of edges in an $n$-vertex planar graph which does not contain any member of $\mathcal{F}$ as a subgraph. In this paper, we give upper bounds of $ex_{\mathcal{P}}(n,\{K_4,Θ_5\})\leqslant25/11(n-2)$. We also give constructions which show the bounds are tight for infinitely many graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The planar Turán number of $\{K_4,Θ_5\}$ Fang, Tao Combinatorics Let $\mathcal{F}$ be a set of graphs. The planar Turán number, $ex_{\mathcal{P}}(n,\mathcal{F})$, is the maximum number of edges in an $n$-vertex planar graph which does not contain any member of $\mathcal{F}$ as a subgraph. In this paper, we give upper bounds of $ex_{\mathcal{P}}(n,\{K_4,Θ_5\})\leqslant25/11(n-2)$. We also give constructions which show the bounds are tight for infinitely many graphs. |
| title | The planar Turán number of $\{K_4,Θ_5\}$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.05507 |