报告题目：Bisections for some graphs
报告人：丽水学院，颜娟副教授
报告时间: 2021年7月19日9:00-12:00
报告地点：科技园阳光楼南815
报告摘要：
A \emph{bipartition} of $G$ is a bipartition of $V(G)$ with $V(G)=V_1\cup V_2$ and $V_1\cap V_2=\emptyset$. If a bipartition satisfies $||V_1|-|V_2||\leq 1$, we call it a \emph{bisection}. We use $d_G(v)$ to denote the degree of the vertex $v$ in graph $G$. More specifically, for a vertex $v\in V_i$, let $N_{in}(v)=\{u\in V_{i}\mid uv\in E(G)\}$ and $N_{out}(v)=\{u\in V_{3-i}\mid uv\in E(G)\}$. Let $d_{in}(v)=|N_{in}(v)|$ and $d_{out}(v)=|N_{out}(v)|$, and we call them internal degree and external degree of $v$, respectively. Bollob\'{a}s and Scott made the a conjecture concerning the internal degree and external degree of any vertex $v\in V(G)$: Every graph $G$ has a bisection $V(G)=V_1\cup V_2$ such that for any $v\in V(G)$, $d_{out}(v)\geq d_{in}(v)-1.$ In this talk, we will show that this conjecture is true for some graphs.
报告人简介：
颜娟，丽水学院副教授，“浙江省高校领军人才培养计划”高层次拔尖人才。于2009年在南京师范大学数学科学学院获博士学位，美国佐治亚理工学院访问学者。主要从事图的划分方面的研究，论文发表在《Journal of Combinatorial Theory, Series B》、《Journal of Graph Theory》、《Discrete Mathematics》等国际权威学术期刊上。主持完成2项国家基金。
