论文标题
使用$（g，f）$ - 因子和$ m $ -tree连接$（m，f'）$ - 因素的存在$ m $ -tree连接$（g，f+f'-m）$ - 因素
The existence of $m$-tree-connected $(g,f+f'-m)$-factors using $(g,f)$-factors and $m$-tree-connected $(m,f')$-factors
论文作者
论文摘要
让$ g $为图，让$ g $，$ f $和$ f'$是$ g \ le f $的$ v（g）$上的三个正整数值函数。 Tokuda，Xu和Wang（2003）表明，如果$ g $包含$（g，f）$ - 因子和一个跨度$ f'$ - 树，则$ g $也包含连接的$（g，f+f'-1）$ - 因子。在本说明中，我们通过证明$ g $包含$（g，f）$ - 因子和$ m $ - 树连接$（m，f'）$ - 因子，然后$ g $也包含$ m $ m $ m $ m-$ - tree-tree-connected $（G，f+f'-m）$ f fe ge，我们还包含$（g，f'）$ - $ f fe ge ge ge ge ge，我们还将其结果开发为与树连接的版本。此外，我们表明$ g $允许无负。
Let $G$ be a graph and let $g$, $f$, and $f'$ be three positive integer-valued functions on $V(G)$ with $g\le f$. Tokuda, Xu, and Wang (2003) showed that if $G$ contains a $(g,f)$-factor and a spanning $f'$-tree, then $G$ also contains a connected $(g,f+f'-1)$-factor. In this note, we develop their result to a tree-connected version by proving that if $G$ contains a $(g,f)$-factor and an $m$-tree-connected $(m,f')$-factor, then $G$ also contains an $m$-tree-connected $(g,f+f'-m)$-factor, provided that $f\ge m$. In addition, we show that $g$ allows to be nonnegative.
