Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs

  title={Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs},
  author={Gholam Reza Omidi and Maryam Shahsiah},
  journal={SIAM J. Discret. Math.},
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 with the set of $n$ edges $e_i=\{v_{(i-1)(k-1)+1},v_{(i-1)(k-1)+2},\ldots,v_{(i-1)(k-1)+k}\}$, $1\leq i\leq n$, where we use mod $n(k-1)$ arithmetic. The Ramsey number $R(\mathcal{C}^k_n,\mathcal{C}^k_n)$ is asymptotically $\frac{1}{2}(2k-1)n$ as has been proved by Gy\'{a}rf\'{a}s, S\'{a}rk\"{o}zy and Szemer\'{e}di. In this paper, we investigate to determining the exact value of… 
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