论文标题
最小图表及其应用的属性vi：图表$γ_{m+1} $ type $的图表$γ$（M; 2,3,2）$
Properties of minimal charts and their applications VI: the graph $Γ_{m+1}$ in a chart $Γ$ of type $(m;2,3,2)$
论文作者
论文摘要
令$γ$为图表，我们用$γ_m$表示标签$ m $的所有边缘的结合。图表$γ$是类型$（M; 2,3,2）$如果$ W（γ）= 7 $，$ W（γ_M\capγ_{m+1}）= 2 $，$ W（γ_{m+1} \capγ_{m+2}） $ w（g）$是$ g $中的白色顶点的数量。在本文中，我们证明，如果有最小的图表$γ$ type $（m; 2,3,2）$，则$γ_{m+1} $中的每一个，$γ_{m+2} $包含三种图形之一。在下一篇论文中，我们将证明没有最小的$ $（M; 2,3,2）$的图表。
Let $Γ$ be a chart, and we denote by $Γ_m$ the union of all the edges of label $m$. A chart $Γ$ is of type $(m;2,3,2)$ if $w(Γ)=7$, $w(Γ_m\capΓ_{m+1})=2$, $w(Γ_{m+1}\capΓ_{m+2})=3$, and $w(Γ_{m+2}\capΓ_{m+3})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we prove that if there is a minimal chart $Γ$ of type $(m;2,3,2)$, then each of $Γ_{m+1}$ and $Γ_{m+2}$ contains one of three kinds of graphs. In the next paper, we shall prove that there is no minimal chart of type $(m;2,3,2)$.
