论文标题
一个奇数$ [1，b] $ - eigenvalues的常规图中的因素
An odd $[1,b]$-factor in regular graphs from eigenvalues
论文作者
论文摘要
奇数$ [1，b] $ - 图$ g $的因子是一个子图$ h $，因此对于每个顶点$ v \ in v（g）$，$ d_h（v）$ as ODD和$ 1 \ le d_h（v）\ le b $。令$λ_3（g）$为$ g $的邻接矩阵的第三大特征值。对于正整数而言，$ r \ ge 3 $甚至$ n $，lu，wu和yang [10]在$ n $ n $ vertex $ r $ r $ r $ r $ r $ g $ gurantee中的$λ_3（g）$的下限证明是一个奇数$ [1，b] $ in $ g $ in $ g $中的。在本文中，我们改善了界限；每$ r $都是锋利的。
An odd $[1,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for each vertex $v \in V(G)$, $d_H(v)$ is odd and $1\le d_H(v) \le b$. Let $λ_3(G)$ be the third largest eigenvalue of the adjacency matrix of $G$. For positive integers $r \ge 3$ and even $n$, Lu, Wu, and Yang [10] proved a lower bound for $λ_3(G)$ in an $n$-vertex $r$-regular graph $G$ to gurantee the existence of an odd $[1,b]$-factor in $G$. In this paper, we improve the bound; it is sharp for every $r$.
