An improved upper bound for planar Turán number of double star $S_{2,5}$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929480454373376 |
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| author | Xu, Xin Hu, Yue Zhang, Xu |
| author_facet | Xu, Xin Hu, Yue Zhang, Xu |
| contents | The planar Turán number of a graph $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $n$-vertex $H$-free planar graph. Recently, D. Ghosh, et al. initiated the topic of double stars and prove that $ex_{\mathcal{P}}(n,S_{2,5})\leq \frac{20}{7}n$. In this paper, we continue to study this and give a sharp upper bound $ex_{\mathcal{P}}(n,S_{2,5})\leq \frac{19}{7}n-\frac{18}{7}$ for all $n\geq 1$, with equality when $n=12$. This improves Ghosh's result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An improved upper bound for planar Turán number of double star $S_{2,5}$ Xu, Xin Hu, Yue Zhang, Xu Combinatorics The planar Turán number of a graph $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $n$-vertex $H$-free planar graph. Recently, D. Ghosh, et al. initiated the topic of double stars and prove that $ex_{\mathcal{P}}(n,S_{2,5})\leq \frac{20}{7}n$. In this paper, we continue to study this and give a sharp upper bound $ex_{\mathcal{P}}(n,S_{2,5})\leq \frac{19}{7}n-\frac{18}{7}$ for all $n\geq 1$, with equality when $n=12$. This improves Ghosh's result. |
| title | An improved upper bound for planar Turán number of double star $S_{2,5}$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.11060 |