arXiv
Open Access
2022
Planar Turán number of disjoint union of $C_3$ and $C_4$
Ping Li
Abstrak
The {\em planar Turán number} of $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $H$-free planar graph. The planar Turán number of $k\geq 3$ vertex-disjoint union of cycles is a trivial value $3n-6$. Lan, Shi and Song determine the exact value of $ex_{\mathcal{P}}(n,2C_3)$. We continue to study planar Turán number of vertex-disjoint union of cycles and obtain the exact value of $ex_{\mathcal{P}}(n,H)$, where $H$ is vertex-disjoint union of $C_3$ and $C_4$. The extremal graphs are also characterized. We also improve the lower bound of $ex_{\mathcal{P}}(n,2C_k)$ when $k$ is sufficiently large.
Topik & Kata Kunci
Penulis (1)
P
Ping Li
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2022
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- en
- Sumber Database
- arXiv
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- Open Access ✓