论文标题
$ k $ - 扩展性的光谱条件和$ k $ - 两部分图的因素
Spectral conditions for $k$-extendability and $k$-factors of bipartite graphs
论文作者
论文摘要
令$ g $为连接的图。如果$ g $包含尺寸$ k $的匹配，并且每种尺寸$ k $的匹配都包含在$ g $的完美匹配中，则$ g $被认为为\ emph {$ k $ - extendable}。 $ k $ - $ g $的跨度子图称为\ textit {$ k $ -factor}。在本文中，我们为（平衡的两部分）图提供了频谱条件，最低度$δ$为$ k $ - 延迟，并且分别在平衡的两部分图中存在$ k $ factor。我们的结果将一些先前的结果概括为图形的完美匹配，并将结果扩展为\ cite {d.f}和\ cite {w.l}到$ k $ - extendable图。此外，我们的结果概括了lu，liu和tian \ cite {lu-liu}的结果。此外，使用$ k $ edge-dissexhint的等效性完美匹配和$ k $ - $ k $ - 均衡的两部分图，我们的结果可以得出频谱条件，用于在平衡的两部分图中存在$ k $ edge-edise-exch-disexexexhip perfect匹配。
Let $G$ be a connected graph. If $G$ contains a matching of size $k$, and every matching of size $k$ is contained in a perfect matching of $G$, then $G$ is said to be \emph{$k$-extendable}. A $k$-regular spanning subgraph of $G$ is called a \textit{$k$-factor}. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree $δ$ to be $k$-extendable, and for the existence of a $k$-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in \cite{D.F} and \cite{W.L} to $k$-extendable graphs. Furthermore, our results generalize the result of Lu, Liu and Tian \cite{Lu-Liu} to general regular factors. Additionally, using the equivalence of $k$ edge-disjoint perfect matchings and $k$-factors in balanced bipartite graphs, our results can derive a spectral condition for the existence of $k$ edge-disjoint perfect matchings in balanced bipartite graphs.
