### Abstract

In 2006, Kühn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767 821] showed that if a 3-graph H on n vertices has minimum codegree at least (1/4 + o(1))n and n is even, then H has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of n/4 suffices. The result is tight.

Original language | English (US) |
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Pages (from-to) | 67-76 |

Number of pages | 10 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Absorbing lemma
- Hamilton cycle
- Hypergraphs

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Tight codegree condition for the existence of loose hamilton cycles in 3-graphs.** / Czygrinow, Andrzej; Molla, Theodore.

Research output: Contribution to journal › Article

*SIAM Journal on Discrete Mathematics*, vol. 28, no. 1, pp. 67-76. https://doi.org/10.1137/120890417

}

TY - JOUR

T1 - Tight codegree condition for the existence of loose hamilton cycles in 3-graphs

AU - Czygrinow, Andrzej

AU - Molla, Theodore

PY - 2014

Y1 - 2014

N2 - In 2006, Kühn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767 821] showed that if a 3-graph H on n vertices has minimum codegree at least (1/4 + o(1))n and n is even, then H has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of n/4 suffices. The result is tight.

AB - In 2006, Kühn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767 821] showed that if a 3-graph H on n vertices has minimum codegree at least (1/4 + o(1))n and n is even, then H has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of n/4 suffices. The result is tight.

KW - Absorbing lemma

KW - Hamilton cycle

KW - Hypergraphs

UR - http://www.scopus.com/inward/record.url?scp=84898900628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898900628&partnerID=8YFLogxK

U2 - 10.1137/120890417

DO - 10.1137/120890417

M3 - Article

AN - SCOPUS:84898900628

VL - 28

SP - 67

EP - 76

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 1

ER -