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- W2964129664 abstract "A $k$-uniform loose cycle $mathcal{C}_n^k$ is a hypergraph with vertex set ${v_1,v_2,ldots,v_{n(k-1)}}$ and the set of $n$ edges $e_i={v_{(i-1)(k-1)+1},v_{(i-1)(k-1)+2},ldots, v_{(i-1)(k-1)+k}}$, $1leq ileq n$, where we use mod $n(k-1)$ arithmetic. The diagonal Ramsey number of $mathcal{C}^k_n$, $R(mathcal{C}^k_n,mathcal{C}^k_n)$, is asymptotically $frac{1}{2}(2k-1)n$, as has been proved by Gyárfás, Sárközy, and Szemerédi [Electron. J. Combin., 15 (2008), #R126]. In this paper, we investigate to determine the exact value of $R(mathcal{C}^k_n,mathcal{C}^k_n)$ and we show that for $ngeq 2$ and $kgeq 8,$ $R(mathcal{C}^k_n,mathcal{C}^k_n)=(k-1)n+lfloorfrac{n-1}{2}rfloor.$" @default.
- W2964129664 created "2019-07-30" @default.
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- W2964129664 date "2017-01-01" @default.
- W2964129664 modified "2023-09-29" @default.
- W2964129664 title "Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs" @default.
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- W2964129664 doi "https://doi.org/10.1137/16m1077647" @default.
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