Properties of minimal charts and their applications VIII: charts of type (7)

2021/10/20 by Teruo Nagase, Nagase, Teruo, Akiko Shima +1
Computer Science · Engineering · #05C10(Primary) 57M15(Secondary) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2110.10467

openalex publication_date 2021/10/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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 (7) if there exists a label m such that w(Γ)=7, w(Γ_m∩Γ_m+1)=7 where w(G) is the number of white vertices in G. In this paper, we prove that there is no minimal chart of type (7).

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