2023-01-29T05:10:12Z https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:02005207 2022-12-19T05:36:49Z 312:6865:1655967293406:1655967376130 9:504:6868:1655967151838:1655967215050
Properties of Minimal Charts and their Applications VI : The Graph {\Large\$\boldsymbol{\Gamma_{m+1}}\$} in a Chart {\Large\$\boldsymbol{\Gamma}\$} of Type {\Large\$\boldsymbol{(m;2,3,2)}\$ Nagase , Teruo Shima, Akiko Surface link chart white vertex 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 \$(m;2,3,2)\$ if \$w(\Gamma)=7\$, \$w(\Gamma_m\cap\Gamma_{m+1})=2\$, \$w(\Gamma_{m+1}\cap\Gamma_{m+2})=3\$, 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 prove that if there is a minimal chart \$\Gamma\$ of type \$(m;2,3,2)\$, then each of \$\Gamma_{m+1}\$ and \$\Gamma_{m+2}\$ contains one of three kinds of graphs. In the next paper, we shall prove that there is no minimal chart of type \$(m;2,3,2)\$. departmental bulletin paper Graduate School of Mathematical Sciences, The University of Tokyo 2020-11-06 application/pdf Journal of Mathematical Sciences The University of Tokyo 1 27 109 156 AA11021653 13405705 https://repository.dl.itc.u-tokyo.ac.jp/record/2005207/files/jms270106.pdf eng