论文标题
在边缘连接图和艰难的图中存在与树连接的$ \ {g，f \} $的存在
The existence of tree-connected $\{g,f\}$-factors in edge-connected graphs and tough graphs
论文作者
论文摘要
在1970年，lov {á} sz为图$ g $中存在一个因子$ f $提供了必要和足够的条件，以使每个顶点$ v $，$ g（v）\ le d_f（v）\ le f（v）\ le f（v）$，其中$ g $和$ g $和$ f $ f $是$ v（g）$ $ g f $ f f $ f fe f $ f fe f $ f。在本文中，我们给出了足够的边缘连接性条件，以在两部分$ g $中存在$ $ m $ -tree连接的因子$ h $，带有两性$（x，y）$，使其补充为$ m_0 $ -m_0 $ -tree-tree-tree-tree-tree-tree-tree-tree-tree-tree-tree-tree-tree-d_h $ v $ v $ v $ v $ v $ v $ d_h（v）$（v）每个顶点$ v $，$ g（v）+m_0 \ le \ frac {1} {2} d_g（v）\ le f（v）-m $和$ | f（v）-g（v）-g（v）| \ le k $，并且有$ h（v） x} h（v）= \ sum_ {v \ in y} h（v）$。此外，我们将此结果推广到一般图。作为一个应用程序，我们为存在树连接的$ \ {g，f \} $的存在提供了足够的条件 - 边缘连接图和艰难图中的因子。
In 1970 Lov{á}sz gave a necessary and sufficient condition for the existence of a factor $F$ in a graph $G$ such that for each vertex $v$, $g(v)\le d_F(v)\le f(v)$, where $g$ and $f$ are two integer-valued functions on $V(G)$ with $g\le f$. In this paper, we give a sufficient edge-connectivity condition for the existence of an $m$-tree-connected factor $H$ in a bipartite graph $G$ with bipartition $(X,Y)$ such that its complement is $m_0$-tree-connected and for each vertex $v$, $d_H(v)\in \{g(v),f(v)\}$, provided that for each vertex $v$, $g(v)+m_0\le \frac{1}{2}d_G(v)\le f(v)-m$ and $|f(v)-g(v)|\le k$, and there is $h(v)\in \{g(v),f(v)\}$ in which $\sum_{v\in X}h(v)=\sum_{v\in Y}h(v)$. Moreover, we generalize this result to general graphs. As an application, we give sufficient conditions for the existence of tree-connected $\{g,f\}$-factors in edge-connected graphs and tough graphs.
