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

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