### Abstract

The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n/4. The result is proved with the Regularity Lemma via the existence of a monochromatic connected matching covering asymptotically 4n/5 vertices in the multicoloured 2-shadow graph induced by the colouring of K_{n}^{(3)}.

Original language | English |
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Pages (from-to) | 53-71 |

Number of pages | 19 |

Journal | Combinatorics Probability and Computing |

Volume | 20 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Gyárfás, A., & Sárközy, G. N. (2011). The 3-colour Ramsey number of a 3-uniform berge cycle.

*Combinatorics Probability and Computing*,*20*(1), 53-71. https://doi.org/10.1017/S0963548310000209