报告方式：线上报告，腾讯会议号583 259 784
邀请人：常虹
摘要：
For each surface $\Sigma$, we define $\Delta(\Sigma)=\max\{\Delta(G) | G$ is a class two graph with maximum degree $\Delta(G)$ that can be embedded on $ \Sigma \}$. Hence Vizing's Planar Graph Conjecture can be restated as $\Delta(\Sigma)=5$ if $\Sigma$ is a sphere.For a surface $\Sigma$ with Euler characteristic $\chi$, it is known $\Delta(\Sigma)\ge H(\chi)-1$ where $H(\chiχ)$ is the Heawood number of the surface and if the Euler characteristic $\chi\in\{-7, -6, \cdots, -1, 0\}$, $\Delta(\Sigma)$ is already known. In this paper, we study critical graphs on general surfaces and show that if $G$ is a critical graph embeddable on a surface $\Sigma$ with Euler characteristic $\chi\le -8$, then $\Delta(G)\le H(\chi)$ (or $H(\chi)+1$) for some special families of graphs, namely if the minimum degree is at most $11$ or If $\Delta$ is very large etc. As applications, we show that $\Delta(\Sigma)\le H(\chi)$ if $\chi\in \{-22,-21,\cdots,-8\}\backslash\{-19,-16\}$ and $\Delta(\Sigma)\le H(\chi)+1$ if $\chi\in \{-53,\cdots,-23\}\cup\{-19,-16\}$. Combining this with Jungerman (1974), it follows that if $\chi=-12$ and $\Sigma$ is orientable, then $\Delta(\Sigma)=H(\chi)$. This is joint work with Katie Horacek, Rong Luo and Yue Zhao.
简介：
苗正科，江苏师范大学教授、博士生导师、副校长。主要从事图论研究，先后主持国家自然科学基金面上项目4项，作为主要成员参加国家自然科学基金重点项目1项，发表学术论文100余篇、教学研究论文4篇，获教育部优秀科研成果（科学技术）奖自然科学二等奖1项，获江苏省优秀教学成果奖二等奖2项。担任中国运筹学会常务理事及其图论组合分会副理事长、中国数学会组合数学与图论专业委员会常务委员、中国工业与应用数学学会图论组合及应用专业委员会常务委员等。