Spectral radius, toughness and $k$-factor of graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912977153687552 |
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| author | Chen, Yuanyuan Lin, Huiqiu Li, Shucheng |
| author_facet | Chen, Yuanyuan Lin, Huiqiu Li, Shucheng |
| contents | A $k$-regular spanning subgraph of $G$ is called a $k$-factor. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] presented a tight sufficient condition in terms of the spectral radius for a connected 1-tough graph to contain a connected 2-factor (Hamilton cycle). Then it is interesting to consider the following problem: What is the spectral radius condition to guarantee the existence of a $k$-factor with $k\ge3$ in a connected 1-tough graph $G$ with $δ(G)\ge k$? In this paper, we completely solve this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21577 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral radius, toughness and $k$-factor of graphs Chen, Yuanyuan Lin, Huiqiu Li, Shucheng Combinatorics 05C42, 05C50 A $k$-regular spanning subgraph of $G$ is called a $k$-factor. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] presented a tight sufficient condition in terms of the spectral radius for a connected 1-tough graph to contain a connected 2-factor (Hamilton cycle). Then it is interesting to consider the following problem: What is the spectral radius condition to guarantee the existence of a $k$-factor with $k\ge3$ in a connected 1-tough graph $G$ with $δ(G)\ge k$? In this paper, we completely solve this problem. |
| title | Spectral radius, toughness and $k$-factor of graphs |
| topic | Combinatorics 05C42, 05C50 |
| url | https://arxiv.org/abs/2602.21577 |