Properties of minimal charts and their applications VII: charts of type $(2,3,2)$

Let $\mathrm{\Gamma }$ be a chart, and we denote by ${\mathrm{\Gamma }}_m$ the union of all the edges of label $m$. A chart $\mathrm{\Gamma }$ is of type $(2,3,2)$ if there exists a label $m$ such that $w(\mathrm{\Gamma })=7$, $w({\mathrm{\Gamma }}_m\cap {\mathrm{\Gamma }}_{m+1})=2$, $w({\mathrm{\Gamma }}_{m+1}\cap {\mathrm{\Gamma }}_{m+2})=3$, and $w({\mathrm{\Gamma }}_{m+2}\cap {\mathrm{\Gamma }}_{m+3})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we prove that there is no minimal chart of type $(2,3,2)$.