Regular factors of regular graphs from eigenvalues
发布时间：2025-04-30
点击次数：
- 发布时间：
- 2025-04-30
- 论文名称：
- Regular factors of regular graphs from eigenvalues
- 发表刊物：
- Electronic J. Combinatorics
- 摘要：
- Let $r$ and $m$ be two integers such that $rgeq m$. Let $H$ be a
graph with order $|H|$, size $e$ and maximum degree $r$ such that
$2egeq |H|r-m$. We find a best lower bound on spectral radius of
graph $H$ in terms of $m$ and $r$. Let $G$ be a connected
$r$-regular graph of order $|G|$ and $ k<r$ be an integer. Using the
previous results, we find some best upper bounds (in terms of $r$
and $k$) on the third largest eigenvalue that is sufficient to
guarantee that $G$ has a $k$-factor when $k|G|$ is even. Moreover,
we find a best bound on the second largest eigenvalue that is
sufficient to guarantee that $G$ is $k$-critical when $k|G|$ is odd.
Our results extend the work of Cioabu{a}, Gregory and Haemers
cite{Cio3} who obtained such results for 1-factors.
- 合写作者：
- H. Lu
- 是否译文：
- 否
- 发表时间：
- 2010-11-27