### Abstract

We show that every 3-uniform hypergraph with n vertices and minimum vertex degree at least (5/9 + o(1)) (n 2) contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal.

Original language | English |
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Journal | Proceedings of the London Mathematical Society |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- 05C45
- 05C65 (primary)
- 05D05 (secondary)

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*. https://doi.org/10.1112/plms.12235

**Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs.** / Reiher, Christian; Rödl, Vojtěch; Ruciński, Andrzej; Schacht, Mathias; Szemerédi, E.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*. https://doi.org/10.1112/plms.12235

}

TY - JOUR

T1 - Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs

AU - Reiher, Christian

AU - Rödl, Vojtěch

AU - Ruciński, Andrzej

AU - Schacht, Mathias

AU - Szemerédi, E.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We show that every 3-uniform hypergraph with n vertices and minimum vertex degree at least (5/9 + o(1)) (n 2) contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal.

AB - We show that every 3-uniform hypergraph with n vertices and minimum vertex degree at least (5/9 + o(1)) (n 2) contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal.

KW - 05C45

KW - 05C65 (primary)

KW - 05D05 (secondary)

UR - http://www.scopus.com/inward/record.url?scp=85061437199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061437199&partnerID=8YFLogxK

U2 - 10.1112/plms.12235

DO - 10.1112/plms.12235

M3 - Article

AN - SCOPUS:85061437199

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

ER -