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

Teruo Nagase, Akiko Shima

Let $\Gamma$ be a chart, and we denote by ${\Gamma }_m$ the union of all the edges of label $m$. A chart $\Gamma$ is of type $(3,2,2)$ if there exists a label $m$ such that $w(\Gamma )=7$, $w(Γ_m\capΓ_{m+…