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                1月7日 宋梓霞教授学术报告(数学与统计学院)


                报 告 人: 宋梓霞 教授

                报告题目:Ramsey numbers of cycles under Gallai colorings





                       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。


                       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.