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- W2528123005 abstract "Let $Hxrightarrow{s} G$ denote that any $s$-coloring of $E(H)$ contains a monochromatic $G$. The degree Ramsey number of a graph $G$, denoted by $R_Delta(G, s)$, is $min {Delta(H): H xrightarrow{s} G }$. We consider degree Ramsey numbers where $G$ is a fixed even cycle. Kinnersley, Milans, and West showed that $R_Delta(C_{2k},s) geq 2s$, and Kang and Perarnau showed that $R_Delta(C_4, s) = Theta(s^2)$. Our main result is that $R_Delta(C_6, s) = Theta(s^{3/2})$ and $R_Delta(C_{10}, s) = Theta(s^{5/4})$. Additionally, we substantially improve the lower bound for $R_Delta(C_{2k}, s)$ for general $k$." @default.
- W2528123005 created "2016-10-14" @default.
- W2528123005 creator A5054251227 @default.
- W2528123005 date "2016-10-03" @default.
- W2528123005 modified "2023-09-27" @default.
- W2528123005 title "Degree Ramsey numbers for even cycles" @default.
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- W2528123005 hasPublicationYear "2016" @default.
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