Seminar on Discrete Mathematics: Results on Ramsey number and Gallai-Ramsey number of graphs with small chromatic numbers

：卫兵（美国密西西比大学）
：2023-12-25 16:00
：海韵园数理大楼686会议室

报告人：卫兵（美国密西西比大学）

时  间：2023年12月25日16:00

地  点：海韵园数理大楼686会议室

内容摘要:

A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given a graph $H$ and an integer $k\ge1$, the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every Gallai $k$-coloring of the edges of $K_n$ contains a monochromatic copy of $H$. If $k=2$, $GR_2(G)$ is the classical Ramsey number, which means that Gallai-Ramsey number is a generalization of Ramsey number. In this talk, we present some of our recent results on the upper and lower bounds of Ramsey numbers and Gallai-Ramsey numbers for graphs with small chromatic numbers such as $\widehat{K}_m$ for $m\ge2$, where $\widehat{K}_m$ is a kipas with $m+1$ vertices obtained from the join of $K_1$ and a path $P_m$, $W_n$ (a wheel with $n+1$ vertices) obtained  from the join of  $K_1$ and a cycle $C_n$, and some graphs with small number of vertices. Exact values of Gallai-Ramsey numbers for some special graphs will also be provided. Our outcomes generalize several recent results which are obtained individually in different published papers.

个人简介：

卫兵，现为美国密西西比大学数学系教授、研究生项目负责人，1992年博士毕业于德国柏林工业大学（Technical University of Berlin）。主要从事图的结构性理论、图的参数以及极图理论等方面的研究工作。在对图的圈，路和因子的结构，图的控制数，图的独立多项式等问题的研究中，获得一些深刻的结果。目前已在J. Combin. Theory, Ser. B, J. Graph Theory等期刊上发表科研论文九十余篇；若干国际SCI杂志的专业审稿人；应邀在国际或国内多个学术研究机构从事合作研究。在国内工作期间，曾获得博士后基金、多项国家自然科学基金、留学回国人员基金，香港裘槎基金等项目的资助等；曾经担任中国运筹学会副秘书长、中国图论学会秘书长；曾任中科院研究员、博士生导师。

 

联系人：金贤安