报 告 人：Songling Shan 博士
报告题目：The Core Conjecture of Hilton and Zhao and Beyond
报告时间：2020年12月18日（周五）晚上：9:00-10:00
报告地点：腾讯会议（会议 ID：972 762 316）
主办单位：数学与统计学院、科学技术研究院
报告人简介：
Songling Shan 博士于2014年毕业于Georgia State University, 获理学博士学位，师从陈冠涛教授，主要研究方向是图论及组合，具体包括图的结构，图染色及极值图论。2015年至2018年在Vanderbilt University 做 Mark Ellingham 教授的博士后。现在是Illinois State University 助理教授。已在J. Graph Theory, SIAM J. Discrete Math., J.Combin. Theory Ser. B 等国际期刊发表学术论文20余篇。
报告摘要：
Let $G$ be a simple graph with maximum degree $\Delta$. We call $G$ \emph{overfull} if $|E(G)|>\Delta \lfloor |V(G)|/2\rfloor$. The \emph{core} of $G$, denoted $G_{\Delta}$, is the subgraph of $G$ induced by its vertices of degree $\Delta$. A classical result of Vizing shows that $\chi'(G)$, the chromatic index of $G$, is either $\Delta$ or $\Delta+1$. It is NP-complete to determine the chromatic index for a general graph. However, $\chi'(G)=\Delta+1$ if $G$ is overfull. Hilton and Zhao in 1996 conjectured that if $G$ is a simple connected graph with $\Delta\ge 3$ and $\Delta(G_\Delta)\le 2$, then $\chi'(G)=\Delta+1$ if and only if $G$ is overfull or $G=P^*$, where $P^*$ is obtained from the Petersen graph by deleting a vertex. The progress on the conjecture has been slow: it was only confirmed for $\Delta=3,4$, respectively, in 2003 and 2017. In this talk, we will take about the confirmation of this conjecture for all $\Delta\ge 4$ and the more general overfull graph conjecture.
