Sufficient conditions for even factors in graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917357422641152 |
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| author | Zhou, Sizhong Bian, Qiuxiang Wu, Jiancheng |
| author_facet | Zhou, Sizhong Bian, Qiuxiang Wu, Jiancheng |
| contents | Let $G$ be a graph. We denote by $e(G)$ and $ρ(G)$ the size and the spectral radius of $G$. A spanning subgraph $F$ of $G$ is called an even factor of $G$ if $d_F(v)\in\{2,4,6,\ldots\}$ for every $v\in V(G)$. Yan and Kano provided a sufficient condition using the number of odd components in $G-S$ for a graph $G$ of even order to contain an even factor, where $S$ is a vertex subset of $G$ [Z. Yan, M. Kano, Strong Tutte type conditions and factors of graphs, Discuss. Math. Graph Theory 40 (2020) 1057--1065]. In this paper, motivated by Yan and Kano's above result, we present some tight sufficient conditions to guarantee that a connected graph $G$ with the minimum degree $δ$ contains an even factor with respect to its size and spectral radius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sufficient conditions for even factors in graphs Zhou, Sizhong Bian, Qiuxiang Wu, Jiancheng Combinatorics 05C50, 05C70 Let $G$ be a graph. We denote by $e(G)$ and $ρ(G)$ the size and the spectral radius of $G$. A spanning subgraph $F$ of $G$ is called an even factor of $G$ if $d_F(v)\in\{2,4,6,\ldots\}$ for every $v\in V(G)$. Yan and Kano provided a sufficient condition using the number of odd components in $G-S$ for a graph $G$ of even order to contain an even factor, where $S$ is a vertex subset of $G$ [Z. Yan, M. Kano, Strong Tutte type conditions and factors of graphs, Discuss. Math. Graph Theory 40 (2020) 1057--1065]. In this paper, motivated by Yan and Kano's above result, we present some tight sufficient conditions to guarantee that a connected graph $G$ with the minimum degree $δ$ contains an even factor with respect to its size and spectral radius. |
| title | Sufficient conditions for even factors in graphs |
| topic | Combinatorics 05C50, 05C70 |
| url | https://arxiv.org/abs/2510.10500 |