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Zi-Xia Song (宋梓霞), Ramsey numbers of cycles under Gallai colorings

Tuesday, October 15, 2019 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)


Zi-Xia Song (宋梓霞)
Department of Mathematics, University of Central Florida

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.

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


Tuesday, October 15, 2019
4:30 PM - 5:30 PM KST
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Room B232
IBS (기초과학연구원)


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IBS 이산수학그룹 Discrete Mathematics Group
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