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arXiv 2402.136012024-02math.CO

图具有强奇偶因子的谱条件

A spectral condition for a graph having a strong parity factor

Sizhong Zhou, Tao Zhang, Qiuxiang Bian

备注：: 11 pages
发表信息：: Discrete Applied Mathematics 360(2025)188-195

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AI总结：

该研究针对图的强奇偶因子存在性问题，提出了一种谱半径条件，可用于判定连通图是否包含强奇偶因子，为图论中相关奇偶因子问题的研究提供了谱方法视角的结论。

摘要：

若对每个满足|X|为偶数的顶点子集X⊆V(G)，图G都存在生成子图F，满足δ(F)≥1，且对任意u∈X有d_F(u)≡1 (mod 2)，对任意v∈V(G)\X有d_F(v)≡0 (mod 2)，则称G包含强奇偶因子F。本文给出了保证连通图包含强奇偶因子的谱半径条件。

英文摘要：

A graph $G$ contains a strong parity factor $F$ if for every subset $X\subseteq V(G)$ with $|X|$ even, $G$ has a spanning subgraph $F$ satisfying $δ(F)\geq1$, $d_F(u)\equiv1$ (mod 2) for any $u\in X$, and $d_F(v)\equiv0$ (mod 2) for any $v\in V(G)\setminus X$. In this paper, we give a spectral radius condition to guarantee that a connected graph contains a strong parity factor.

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