Saturation Numbers for Linear Forests $P_7+tP_2$
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913467004354560 |
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| author | Zhang, Yu Hao, Rong-Xia He, Zhen Zhu, Wen-Han |
| author_facet | Zhang, Yu Hao, Rong-Xia He, Zhen Zhu, Wen-Han |
| contents | Let $H$ be a fixed graph, a graph G is $H$-saturated if it has no copy of $H$ in $G$, but the addition of any edge in $E(\overline G)$ to $G$ results in an $H$-subgraph. The saturation number sat$(n,H)$ is the minimum number of edges in an $H$-saturated graph on $n$ vertices. In this paper, we determine the saturation number sat$(n,P_7+tP_2)$ for $n\geq \frac {14}{5}t+27$ and characterize the extremal graphs for $n\geq \frac{14}{13}(3t+25)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Saturation Numbers for Linear Forests $P_7+tP_2$ Zhang, Yu Hao, Rong-Xia He, Zhen Zhu, Wen-Han Combinatorics 05C35 Let $H$ be a fixed graph, a graph G is $H$-saturated if it has no copy of $H$ in $G$, but the addition of any edge in $E(\overline G)$ to $G$ results in an $H$-subgraph. The saturation number sat$(n,H)$ is the minimum number of edges in an $H$-saturated graph on $n$ vertices. In this paper, we determine the saturation number sat$(n,P_7+tP_2)$ for $n\geq \frac {14}{5}t+27$ and characterize the extremal graphs for $n\geq \frac{14}{13}(3t+25)$. |
| title | Saturation Numbers for Linear Forests $P_7+tP_2$ |
| topic | Combinatorics 05C35 |
| url | https://arxiv.org/abs/2408.06719 |