### Abstract

A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which every three consecutive vertices form an edge. In this paper we prove an approximate and asymptotic version of an analogue of Dirac's celebrated theorem for graphs: for each γ>0 there exists n_{0} such that every 3-uniform hypergraph on $n\geq n_0$ vertices, in which each pair of vertices belongs to at least $(1/2+\gamma)n$ edges, contains a Hamiltonian cycle.

Original language | English |
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Pages (from-to) | 229-251 |

Number of pages | 23 |

Journal | Combinatorics Probability and Computing |

Volume | 15 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jan 2006 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Statistics and Probability

### Cite this

*Combinatorics Probability and Computing*,

*15*(1-2), 229-251. https://doi.org/10.1017/S0963548305007042

**A dirac-type theorem for 3-uniform hypergraphs.** / Rödl, Vojtěch; Ruciński, Andrzej; Szemerédi, E.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 15, no. 1-2, pp. 229-251. https://doi.org/10.1017/S0963548305007042

}

TY - JOUR

T1 - A dirac-type theorem for 3-uniform hypergraphs

AU - Rödl, Vojtěch

AU - Ruciński, Andrzej

AU - Szemerédi, E.

PY - 2006/1

Y1 - 2006/1

N2 - A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which every three consecutive vertices form an edge. In this paper we prove an approximate and asymptotic version of an analogue of Dirac's celebrated theorem for graphs: for each γ>0 there exists n0 such that every 3-uniform hypergraph on $n\geq n_0$ vertices, in which each pair of vertices belongs to at least $(1/2+\gamma)n$ edges, contains a Hamiltonian cycle.

AB - A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which every three consecutive vertices form an edge. In this paper we prove an approximate and asymptotic version of an analogue of Dirac's celebrated theorem for graphs: for each γ>0 there exists n0 such that every 3-uniform hypergraph on $n\geq n_0$ vertices, in which each pair of vertices belongs to at least $(1/2+\gamma)n$ edges, contains a Hamiltonian cycle.

UR - http://www.scopus.com/inward/record.url?scp=29744437708&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29744437708&partnerID=8YFLogxK

U2 - 10.1017/S0963548305007042

DO - 10.1017/S0963548305007042

M3 - Article

AN - SCOPUS:29744437708

VL - 15

SP - 229

EP - 251

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 1-2

ER -