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DTSTART;TZID=Asia/Seoul:20191015T163000
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SUMMARY:Zi-Xia Song (宋梓霞)\, Ramsey numbers of  cycles under Gallai colorings
DESCRIPTION:For a graph $H$ and an integer $k\ge1$\, 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\ge4 $ vertices. For odd cycles\, Bondy and Erd\H{o}s in 1973 conjectured that for all $k\ge1$ and $n\ge2$\, $R_k(C_{2n+1})=n\cdot 2^k+1$. 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 $R_k(C_{2n})$ in general. In this talk we will present our recent results on Ramsey numbers of cycles under Gallai colorings\, where a Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles. We prove that the aforementioned conjecture holds for all $k$ and all $n$ under Gallai colorings. We also completely determine the Ramsey number of even cycles under Gallai colorings. \nJoint work with Dylan Bruce\, Christian Bosse\, Yaojun Chen and Fangfang Zhang.
URL:https://dimag.ibs.re.kr/event/2019-10-15/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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