Some sufficient conditions for graphs to have component factors
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912065119059968 |
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| author | Zhou, Sizhong |
| author_facet | Zhou, Sizhong |
| contents | Let $G$ denote a graph and $k\geq2$ be an integer. A $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$-factor of $G$ is a spanning subgraph, whose every connected component is isomorphic to an element of $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$, where $\mathcal{T}(2k+1)$ is one special family of tree. In this paper, we put forward some sufficient conditions for the existence of $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$-factors in graphs. Furthermore, we construct some extremal graphs to show that the main results in this paper are best possible. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_06829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some sufficient conditions for graphs to have component factors Zhou, Sizhong Combinatorics 05C70, 05C50 Let $G$ denote a graph and $k\geq2$ be an integer. A $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$-factor of $G$ is a spanning subgraph, whose every connected component is isomorphic to an element of $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$, where $\mathcal{T}(2k+1)$ is one special family of tree. In this paper, we put forward some sufficient conditions for the existence of $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$-factors in graphs. Furthermore, we construct some extremal graphs to show that the main results in this paper are best possible. |
| title | Some sufficient conditions for graphs to have component factors |
| topic | Combinatorics 05C70, 05C50 |
| url | https://arxiv.org/abs/2410.06829 |