### Abstract

Here we prove that for n ≥ 140, in every 3-coloring of the edges of K_{n}^{(4)} there is a monochromatic Berge cycle of length at least n - 10. This result sharpens an asymptotic result obtained earlier. Another result is that for n ≥ 15, in every 2-coloring of the edges of K_{n}^{(4)} there is a 3-tight Berge cycle of length at least n - 10.

Original language | English |
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Pages (from-to) | 71-76 |

Number of pages | 6 |

Journal | Graphs and Combinatorics |

Volume | 26 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2010 |

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### Keywords

- Colored complete uniform hypergraphs
- Monochromatic Hamiltonian Berge-cycles

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Graphs and Combinatorics*,

*26*(1), 71-76. https://doi.org/10.1007/s00373-010-0908-y

**Long monochromatic berge cycles in colored 4-uniform hypergraphs.** / Gyárfás, A.; Sárközy, Gábor N.; Szemerédi, E.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 26, no. 1, pp. 71-76. https://doi.org/10.1007/s00373-010-0908-y

}

TY - JOUR

T1 - Long monochromatic berge cycles in colored 4-uniform hypergraphs

AU - Gyárfás, A.

AU - Sárközy, Gábor N.

AU - Szemerédi, E.

PY - 2010/3

Y1 - 2010/3

N2 - Here we prove that for n ≥ 140, in every 3-coloring of the edges of Kn(4) there is a monochromatic Berge cycle of length at least n - 10. This result sharpens an asymptotic result obtained earlier. Another result is that for n ≥ 15, in every 2-coloring of the edges of Kn(4) there is a 3-tight Berge cycle of length at least n - 10.

AB - Here we prove that for n ≥ 140, in every 3-coloring of the edges of Kn(4) there is a monochromatic Berge cycle of length at least n - 10. This result sharpens an asymptotic result obtained earlier. Another result is that for n ≥ 15, in every 2-coloring of the edges of Kn(4) there is a 3-tight Berge cycle of length at least n - 10.

KW - Colored complete uniform hypergraphs

KW - Monochromatic Hamiltonian Berge-cycles

UR - http://www.scopus.com/inward/record.url?scp=77949422928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949422928&partnerID=8YFLogxK

U2 - 10.1007/s00373-010-0908-y

DO - 10.1007/s00373-010-0908-y

M3 - Article

VL - 26

SP - 71

EP - 76

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 1

ER -