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- W4289804500 abstract "Recently Kostochka, Mubayi and Verstraete initiated the study of the Ramsey numbers of uniform loose cycles versus cliques. In particular they proved that $R(C^r_3,K^r_n) = tilde{theta}(n^{3/2})$ for all fixed $rgeq 3$. For the case of loose cycles of length five they proved that $R(C_5^r,K_n^r)=Omega((n/log n)^{5/4})$ and conjectured that $R(C^r_5,K_n^r) = O(n^{5/4})$ for all fixed $rgeq 3$. Our main result is that $R(C_5^3,K_n^3) = O(n^{4/3})$ and more generally for any fixed $lgeq 3$ that $R(C_l^3,K_n^3) = O(n^{1 + 1/lfloor(l+1)/2 rfloor})$. We also explain why for every fixed $lgeq 5$, $rgeq 4$, $R(C^r_l,K^r_n) = O(n^{1+1/lfloor l/2 rfloor})$ if $l$ is odd, which improves upon the result of Collier-Cartaino, Graber and Jiang who proved that for every fixed $rgeq 3$, $lgeq 4$, we have $R(C_l^r,K_n^r) = O(n^{1 + 1/(lfloor l/2 rfloor-1)})$." @default.
- W4289804500 created "2022-08-05" @default.
- W4289804500 creator A5036696949 @default.
- W4289804500 date "2015-04-14" @default.
- W4289804500 modified "2023-09-28" @default.
- W4289804500 title "The Ramsey number of loose cycles versus cliques" @default.
- W4289804500 doi "https://doi.org/10.48550/arxiv.1504.03668" @default.
- W4289804500 hasPublicationYear "2015" @default.
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