Spectral radius and edge-disjoint connected factors of graphs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913156829282304 |
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| author | Tang, Xinying Zhang, Wenqian |
| author_facet | Tang, Xinying Zhang, Wenqian |
| contents | For a graph $G$, the spectral radius of $G$ is the largest eigenvalue of its adjacency matrix. A connected factor of $G$ is a connected spanning subgraph of $G$. For example, a spanning tree of $G$ is a 1-connected factor of $G$. Let $G$ be a graph of order $n$ with minimum degree $δ\geq6$, where $n\geq3δ$. In this paper, we give a sharp spectral radius condition for $G$ to contain $k$ edge-disjoint 2-connected factors and $\left\lfloor\frac{δ-4k}{2}\right\rfloor$ edge-disjoint spanning trees, where $1\leq k\leq\left\lfloor\fracδ{4}\right\rfloor$ is an integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23737 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral radius and edge-disjoint connected factors of graphs Tang, Xinying Zhang, Wenqian Combinatorics For a graph $G$, the spectral radius of $G$ is the largest eigenvalue of its adjacency matrix. A connected factor of $G$ is a connected spanning subgraph of $G$. For example, a spanning tree of $G$ is a 1-connected factor of $G$. Let $G$ be a graph of order $n$ with minimum degree $δ\geq6$, where $n\geq3δ$. In this paper, we give a sharp spectral radius condition for $G$ to contain $k$ edge-disjoint 2-connected factors and $\left\lfloor\frac{δ-4k}{2}\right\rfloor$ edge-disjoint spanning trees, where $1\leq k\leq\left\lfloor\fracδ{4}\right\rfloor$ is an integer. |
| title | Spectral radius and edge-disjoint connected factors of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.23737 |