# A dirac-type theorem for 3-uniform hypergraphs

Vojtěch Rödl, Andrzej Ruciński, E. Szemerédi

Research output: Contribution to journalArticle

104 Citations (Scopus)

### 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 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.

Original language English 229-251 23 Combinatorics Probability and Computing 15 1-2 https://doi.org/10.1017/S0963548305007042 Published - Jan 2006

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Hamiltonians
Uniform Hypergraph
Hamiltonian circuit
Theorem
Consecutive
Analogue
Graph in graph theory

### ASJC Scopus subject areas

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

### Cite this

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

In: Combinatorics Probability and Computing, Vol. 15, No. 1-2, 01.2006, p. 229-251.

Research output: Contribution to journalArticle

Rödl, Vojtěch ; Ruciński, Andrzej ; Szemerédi, E. / A dirac-type theorem for 3-uniform hypergraphs. In: Combinatorics Probability and Computing. 2006 ; Vol. 15, No. 1-2. pp. 229-251.
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