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

Abstract

Let Γ be a chart, and we denote by Γm the union of all the edges of label m. A chart Γ is of type (2,3,2) if there exists a label m such that w(Γ)=7, w(Γm∩Γm+1)=2, w(Γm+1∩Γm+2)=3, and w(Γm+2∩Γm+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).