报告题目：Some results on Gallai-Ramsey numbers of graphs

报告人：卫兵 教授

报告时间：2025年5月23日 15:00-16:00

报告地点：科技园阳光楼南815

邀请单位：数学与统计学院、离散数学及其应用省部共建教育部重点实验室

报告摘要：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 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 $F_n$ (a fan with $2n+1$ vertices) obtained from the join of $K_1$ and a matching with $n$ edges. Exact values of Gallai-Ramsey numbers for some special graphs will also be provided. Further related research problems will be proposed.

This is joint work with Qinghong Zhao.

报告人简介：卫兵，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)。主要从事图的结构理论、图的参数以及极值图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。目前已发表科研论文一百余篇: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。

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