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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.13004 |
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| _version_ | 1866908659054804992 |
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| author | Li, Jiasheng Lv, Xiaoyun Xu, Shoujun |
| author_facet | Li, Jiasheng Lv, Xiaoyun Xu, Shoujun |
| contents | Let $G=(V(G),E(G)) $ be a graph with vertex set $V(G)$ and edge set $E(G)$. An even factor of $G$ is a spanning subgraph $F$ such that every vertex in $F$ has a nonzero even degree. Note that $δ(G)\geq 2$ is a trivial necessary condition for a graph to have an even factor, where \( δ(G) \) is the minimum degree of \( G \). In this paper, for a connected graph $G$ with minimum degree $δ$, we establish a lower bound on the signless
Laplacian spectral radius of $G$ and an upper bound on the distance spectral radius of $G$ such
that $G$ contains an even factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The existence of even factors based on spectral conditions of graphs Li, Jiasheng Lv, Xiaoyun Xu, Shoujun Combinatorics Let $G=(V(G),E(G)) $ be a graph with vertex set $V(G)$ and edge set $E(G)$. An even factor of $G$ is a spanning subgraph $F$ such that every vertex in $F$ has a nonzero even degree. Note that $δ(G)\geq 2$ is a trivial necessary condition for a graph to have an even factor, where \( δ(G) \) is the minimum degree of \( G \). In this paper, for a connected graph $G$ with minimum degree $δ$, we establish a lower bound on the signless Laplacian spectral radius of $G$ and an upper bound on the distance spectral radius of $G$ such that $G$ contains an even factor. |
| title | The existence of even factors based on spectral conditions of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.13004 |