# Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs

@article{Omidi2017DiagonalRN, title={Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs}, author={Gholam Reza Omidi and Maryam Shahsiah}, journal={SIAM J. Discret. Math.}, year={2017}, volume={31}, pages={1634-1669} }

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…

## 3 Citations

Monochromatic loose paths in multicolored k-uniform cliques

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2019

There is an algorithm such that for every $r$-edge-coloring of the edges of the complete $k$-uniform hypergraph, it finds a monochromatic copy of P_\ell^{(k)}$ in time at most $cn^k$.

Cover k-Uniform Hypergraphs by Monochromatic Loose Paths

- MathematicsElectron. J. Comb.
- 2017

It is shown that for every $2$-coloring of the edges of the complete $k-uniform hypergraph, one can find two monochromatic paths of distinct colors to cover all vertices of $\mathcal{K}_n^k$ such that they share at most $ k-2$ vertices.

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