Spectral conditions for graphs to contain $k$-factors
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911097521438720 |
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| author | Tang, Xinying Zhang, Wenqian |
| author_facet | Tang, Xinying Zhang, Wenqian |
| contents | Let $G$ be a graph. The spectral radius $ρ(G)$ of $G$ is the largest eigenvalue of its adjacency matrix. For an integer $k\geq1$, a $k$-factor of $G$ is a $k$-regular spanning subgraph of $G$. Assume that $k$ and $n$ are integers satisfying $k\geq2,kn\equiv0~(\mod2)$ and $n\geq\max\left\{k^{2}+6k+7,20k+10\right\}$. Let $G$ be a graph of order $n$ and with minimum degree at least $k$. In this paper, we give a sharp lower bound of $ρ(G)$ to guarantee that $G$ contains a $k$-factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral conditions for graphs to contain $k$-factors Tang, Xinying Zhang, Wenqian Combinatorics Let $G$ be a graph. The spectral radius $ρ(G)$ of $G$ is the largest eigenvalue of its adjacency matrix. For an integer $k\geq1$, a $k$-factor of $G$ is a $k$-regular spanning subgraph of $G$. Assume that $k$ and $n$ are integers satisfying $k\geq2,kn\equiv0~(\mod2)$ and $n\geq\max\left\{k^{2}+6k+7,20k+10\right\}$. Let $G$ be a graph of order $n$ and with minimum degree at least $k$. In this paper, we give a sharp lower bound of $ρ(G)$ to guarantee that $G$ contains a $k$-factor. |
| title | Spectral conditions for graphs to contain $k$-factors |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.05678 |