Planar Tur\'an number of two adjacent cycles
| Autor: | Li, Luyi, Li, Tong, Song, Xinzhe, Zhou, Qiang |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The planar Tur\'an number of $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum number of edges in an $n$-vertex $H$-free planar graph. The planar Tur\'an number of $k(k\geq 3)$ vertex-disjoint union of cycles is the trivial value $3n-6$. Lan, Shi and Song determined the exact value of $ex_{\mathcal{P}}(n,2C_3)$. In this paper, we further research the existence of two disjoint cycles under distance restriction and get the planar Tur\'an number for $C_3\text{-}C_3$, where $C_{k}\text{-}C_{\ell}$ denotes the graph consisting of two disjoint cycles $C_k$ with an edge connecting them. Comment: 9 pages, 3 figures |
| Databáze: | arXiv |
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