1月7日 宋梓霞教授学术报告(数学与统计学院)

来源:数学科研研究生作者:时间:2020-01-06浏览:912设置

报 告 人: 宋梓霞 教授

报告题目:Ramsey numbers of cycles under Gallai colorings

报告时间:2020年1月7日(周二)下午14:00

报告地点:静远楼1508学术报告厅

主办单位:数学与统计学院、科学技术研究院

报告人简介:

       宋梓霞博士是美国中佛罗里达大学(University of Central Florida)数学系教授,博士生导师。主要研究领域为图论。宋梓霞博士于2000-2004年在美国佐治亚理工大学(Georgia Institute of Technology)获算法,组合,优化(Algorithm, Combinatorics and Optimization)博士学位,2004-2005年在美国俄亥俄州立大学(The Ohio State University)数学系从事博士后研究。2005年授聘于美国中佛罗里达大学数学系。获得2009-2011美国NSA科研基金,是美国自然科学基金(NSF)的基金评委。2013年获校优秀教师奖。

报告摘要:

       For a graph $H$ and an integer $k\geq1$, the $k$-color Ramsey number $R_{k}(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_{N}$ contains a monochromatic copy of $H$. Let $C_{m}$ denote the cycle on $m\geq4$ vertices. For odd cycle, Bondy and Erd\H{o}s in 1973 conjectured that for all $k\geq1$ and $n\geq2$, $R_{k}(C_{2n+1})=n2^{k}+1$.Recently, this conjecture has been verified to be true for all fixed $k$ and all $n$ sufficiently large by Jenssen and Skokan; and false for all fixed $n$ and all $k$ sufficiently large by Day and Johnson. Even cycles behave rather differently in this context. Little is known about the behavior of $R_{k}(C_{2n})$ is general. In this talk we will present our recent results on Ramsey numbers of cycles under Gallai coloring, where a Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles. We also completely determine the Ramsey number of even cycles under Gallai coloring.

Joint work with Dylan Bruce, Christian Bosse, Yaojun Chen and Fangfang Zhang.


返回原图
/