论文标题
途径均匀图的一些足够条件
Some sufficient conditions for path-factor uniform graphs
论文作者
论文摘要
对于连接图的集合$ \ MATHCAL {H} $，如果$ h $的每个组件均为$ h $的每个组成部分，则称为$ g $ $ g $的子图$ h $ of $ g $。图形$ g $称为$ \ MATHCAL {H} $ - 因子均匀图，如果对于任何两个边缘$ e_1 $和$ e_2 $的$ g $，$ g $，$ g $具有$ \ mathcal {h} $ - 覆盖$ e_1 $的因子，不包括$ e_2 $。让$ \ Mathcal {H} $中的每个组件为至少$ d $顶点的路径，其中$ d \ geq2 $是整数。 Then an $\mathcal{H}$-factor and an $\mathcal{H}$-factor uniform graph are called a $P_{\geq d}$-factor and a $P_{\geq d}$-factor uniform graph, respectively.在本文中，我们验证（\ romannumeral1）2-边缘连接的图$ g $是$ p _ {\ geq3} $ - 因子均匀图，如果$δ（g）> \ frac> \ frac {α（g）+4} +4} {2} {2} $; （\ romannumeral2）a $（k+2）$ - 连接的图形$ n $，带有$ n \ geq5k+3- \ 3- \ frac {3} {5γ-1} $是$ p _ {\ geq3} $ - $ n_g（a）$ g $ g $ g $ g $ g $ g+g $ g $ g+g y $ g+k+k+2 $ g+geq3} $ - $ | a | = \lfloorγ（2k+1）\ rfloor $，其中$ k $是一个正整数，$γ$是一个真实的数字，$ \ frac {1} {3} {3} \leqγ\ leq1 $。
For a set $\mathcal{H}$ of connected graphs, a spanning subgraph $H$ of $G$ is called an $\mathcal{H}$-factor of $G$ if each component of $H$ is isomorphic to an element of $\mathcal{H}$. A graph $G$ is called an $\mathcal{H}$-factor uniform graph if for any two edges $e_1$ and $e_2$ of $G$, $G$ has an $\mathcal{H}$-factor covering $e_1$ and excluding $e_2$. Let each component in $\mathcal{H}$ be a path with at least $d$ vertices, where $d\geq2$ is an integer. Then an $\mathcal{H}$-factor and an $\mathcal{H}$-factor uniform graph are called a $P_{\geq d}$-factor and a $P_{\geq d}$-factor uniform graph, respectively. In this article, we verify that (\romannumeral1) a 2-edge-connected graph $G$ is a $P_{\geq3}$-factor uniform graph if $δ(G)>\frac{α(G)+4}{2}$; (\romannumeral2) a $(k+2)$-connected graph $G$ of order $n$ with $n\geq5k+3-\frac{3}{5γ-1}$ is a $P_{\geq3}$-factor uniform graph if $|N_G(A)|>γ(n-3k-2)+k+2$ for any independent set $A$ of $G$ with $|A|=\lfloorγ(2k+1)\rfloor$, where $k$ is a positive integer and $γ$ is a real number with $\frac{1}{3}\leqγ\leq1$.
