Dense $2$-connected planar graphs and the planar Turán number of $2C_k$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910912442531840 |
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| author | Li, Ping |
| author_facet | Li, Ping |
| contents | Shi, Walsh and Yu demonstrated that any dense planar graph with certain property (known as circuit graph) contains a large near-triangulation. We extend the result to $2$-connected plane graphs, thereby addressing a question posed by them. Using the result, we prove that the planar Tuán number of $2C_k$ is $\left[3-Θ(k^{\log_23})^{-1}\right]n$ when $k\geq 5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dense $2$-connected planar graphs and the planar Turán number of $2C_k$ Li, Ping Combinatorics Shi, Walsh and Yu demonstrated that any dense planar graph with certain property (known as circuit graph) contains a large near-triangulation. We extend the result to $2$-connected plane graphs, thereby addressing a question posed by them. Using the result, we prove that the planar Tuán number of $2C_k$ is $\left[3-Θ(k^{\log_23})^{-1}\right]n$ when $k\geq 5$. |
| title | Dense $2$-connected planar graphs and the planar Turán number of $2C_k$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.09367 |